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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 -/
 import CategoryTheory.Limits.KanExtension
-import Topology.Category.Top.Opens
+import Topology.Category.TopCat.Opens
 import CategoryTheory.Adjunction.Opposites
 
 #align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"

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

@@ -3,9 +3,9 @@ Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 -/
-import Mathbin.CategoryTheory.Limits.KanExtension
-import Mathbin.Topology.Category.Top.Opens
-import Mathbin.CategoryTheory.Adjunction.Opposites
+import CategoryTheory.Limits.KanExtension
+import Topology.Category.Top.Opens
+import CategoryTheory.Adjunction.Opposites
 
 #align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
 
@@ -78,7 +78,7 @@ unsafe def restrict_attr : user_attribute (tactic Unit → tactic Unit) Unit
       dependencies := [] }
 #align Top.presheaf.restrict_attr Top.presheaf.restrict_attr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 /-- A tactic to discharge goals of type `U ≤ V` for `Top.presheaf.restrict_open` -/
 unsafe def restrict_tac : ∀ n : ℕ, tactic Unit
   | 0 => tactic.fail "`restrict_tac` failed"

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
-
-! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.KanExtension
 import Mathbin.Topology.Category.Top.Opens
 import Mathbin.CategoryTheory.Adjunction.Opposites
 
+#align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
+
 /-!
 # Presheaves on a topological space
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 13361559d66b84f80b6d5a1c4a26aa5054766725
+! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -322,7 +322,7 @@ open CategoryTheory.Limits
 
 section Pullback
 
-variable [HasColimitsOfSize.{w, w} C]
+variable [HasColimits C]
 
 noncomputable section
 
@@ -333,14 +333,14 @@ This is defined in terms of left Kan extensions, which is just a fancy way of sa
 "take the colimits over the open sets whose preimage contains U".
 -/
 @[simps]
-def pullbackObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
+def pullbackObj {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
   (lan (Opens.map f).op).obj ℱ
 #align Top.presheaf.pullback_obj TopCat.Presheaf.pullbackObj
 -/
 
 #print TopCat.Presheaf.pullbackMap /-
 /-- Pulling back along continuous maps is functorial. -/
-def pullbackMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
+def pullbackMap {X Y : TopCat.{v}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
     pullbackObj f ℱ ⟶ pullbackObj f 𝒢 :=
   (lan (Opens.map f).op).map α
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
@@ -349,7 +349,7 @@ def pullbackMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α :
 #print TopCat.Presheaf.pullbackObjObjOfImageOpen /-
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
-def pullbackObjObjOfImageOpen {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
+def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
     (H : IsOpen (f '' U)) : (pullbackObj f ℱ).obj (op U) ≅ ℱ.obj (op ⟨_, H⟩) :=
   by
   let x : costructured_arrow (opens.map f).op (op U) :=
@@ -373,7 +373,7 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf
 
 namespace Pullback
 
-variable {X Y : TopCat.{w}} (ℱ : Y.Presheaf C)
+variable {X Y : TopCat.{v}} (ℱ : Y.Presheaf C)
 
 #print TopCat.Presheaf.Pullback.id /-
 /-- The pullback along the identity is isomorphic to the original presheaf. -/
@@ -503,13 +503,13 @@ theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf
 
 end Iso
 
-variable (C) [HasColimitsOfSize.{w, w} C]
+variable (C) [HasColimits C]
 
 #print TopCat.Presheaf.pullback /-
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `X`. -/
 @[simps map_app]
-def pullback {X Y : TopCat.{w}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
+def pullback {X Y : TopCat.{v}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
   lan (Opens.map f).op
 #align Top.presheaf.pullback TopCat.Presheaf.pullback
 -/
@@ -525,14 +525,14 @@ theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCa
 #print TopCat.Presheaf.pushforwardPullbackAdjunction /-
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
-def pushforwardPullbackAdjunction {X Y : TopCat.{w}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
+def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
 -/
 
 #print TopCat.Presheaf.pullbackHomIsoPushforwardInv /-
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/
-def pullbackHomIsoPushforwardInv {X Y : TopCat.{w}} (H : X ≅ Y) :
+def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.Hom ≅ pushforward C H.inv :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.Hom)
     (presheafEquivOfIso C H.symm).toAdjunction
@@ -541,7 +541,7 @@ def pullbackHomIsoPushforwardInv {X Y : TopCat.{w}} (H : X ≅ Y) :
 
 #print TopCat.Presheaf.pullbackInvIsoPushforwardHom /-
 /-- Pulling back along the inverse of a homeomorphism is the same as pushing forward along it. -/
-def pullbackInvIsoPushforwardHom {X Y : TopCat.{w}} (H : X ≅ Y) :
+def pullbackInvIsoPushforwardHom {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.inv ≅ pushforward C H.Hom :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.inv)
     (presheafEquivOfIso C H).toAdjunction

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

@@ -102,6 +102,7 @@ example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓
   run_tac
     restrict_tac'
 
+#print TopCat.Presheaf.restrict /-
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
 and the notation `x |_ₗ U ⟪i⟫` (`l` stands for `le`) for `i : U ≤ V`.
@@ -110,16 +111,16 @@ def restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C] {F : X.
     {V : Opens X} (x : F.obj (op V)) {U : Opens X} (h : U ⟶ V) : F.obj (op U) :=
   F.map h.op x
 #align Top.presheaf.restrict TopCat.Presheaf.restrict
+-/
 
--- mathport name: «expr |_ₕ »
 scoped[AlgebraicGeometry] infixl:80 " |_ₕ " => TopCat.Presheaf.restrict
 
--- mathport name: «expr |_ₗ ⟪ ⟫»
 scoped[AlgebraicGeometry]
   notation:80 x " |_ₗ " U " ⟪" e "⟫ " =>
     @TopCat.Presheaf.restrict _ _ _ _ _ _ x U (@homOfLE (Opens _) _ U _ e)
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
+#print TopCat.Presheaf.restrictOpen /-
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ U`, where the proof `U ≤ V` is inferred by
 the tactic `Top.presheaf.restrict_tac'` -/
@@ -131,23 +132,27 @@ abbrev restrictOpen {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     F.obj (op U) :=
   x |_ₗ U ⟪e⟫
 #align Top.presheaf.restrict_open TopCat.Presheaf.restrictOpen
+-/
 
--- mathport name: «expr |_ »
 scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
+#print TopCat.Presheaf.restrict_restrict /-
 @[simp]
 theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
     x |_ V |_ U = x |_ U := by delta restrict_open restrict; rw [← comp_apply, ← functor.map_comp];
   rfl
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
+-/
 
+#print TopCat.Presheaf.map_restrict /-
 @[simp]
 theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
     e.app _ (x |_ U) = e.app _ x |_ U := by delta restrict_open restrict;
   rw [← comp_apply, nat_trans.naturality, comp_apply]
 #align Top.presheaf.map_restrict TopCat.Presheaf.map_restrict
+-/
 
 #print TopCat.Presheaf.pushforwardObj /-
 /-- Pushforward a presheaf on `X` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
@@ -157,21 +162,25 @@ def pushforwardObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) : Y.Pre
 #align Top.presheaf.pushforward_obj TopCat.Presheaf.pushforwardObj
 -/
 
--- mathport name: «expr _* »
 infixl:80 " _* " => pushforwardObj
 
+#print TopCat.Presheaf.pushforwardObj_obj /-
 @[simp]
 theorem pushforwardObj_obj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U : (Opens Y)ᵒᵖ) :
     (f _* ℱ).obj U = ℱ.obj ((Opens.map f).op.obj U) :=
   rfl
 #align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_obj
+-/
 
+#print TopCat.Presheaf.pushforwardObj_map /-
 @[simp]
 theorem pushforwardObj_map {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) {U V : (Opens Y)ᵒᵖ}
     (i : U ⟶ V) : (f _* ℱ).map i = ℱ.map ((Opens.map f).op.map i) :=
   rfl
 #align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_map
+-/
 
+#print TopCat.Presheaf.pushforwardEq /-
 /--
 An equality of continuous maps induces a natural isomorphism between the pushforwards of a presheaf
 along those maps.
@@ -180,6 +189,7 @@ def pushforwardEq {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Preshe
     f _* ℱ ≅ g _* ℱ :=
   isoWhiskerRight (NatIso.op (Opens.mapIso f g h).symm) ℱ
 #align Top.presheaf.pushforward_eq TopCat.Presheaf.pushforwardEq
+-/
 
 #print TopCat.Presheaf.pushforward_eq' /-
 theorem pushforward_eq' {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) :
@@ -187,18 +197,23 @@ theorem pushforward_eq' {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.
 #align Top.presheaf.pushforward_eq' TopCat.Presheaf.pushforward_eq'
 -/
 
+#print TopCat.Presheaf.pushforwardEq_hom_app /-
 @[simp]
 theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq h ℱ).Hom.app U =
       ℱ.map (by dsimp [functor.op]; apply Quiver.Hom.op; apply eq_to_hom; rw [h]) :=
   by simp [pushforward_eq]
 #align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_app
+-/
 
+#print TopCat.Presheaf.pushforward_eq'_hom_app /-
 theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C)
     (U) : NatTrans.app (eqToHom (pushforward_eq' h ℱ)) U = ℱ.map (eqToHom (by rw [h])) := by
   simpa [eq_to_hom_map]
 #align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_app
+-/
 
+#print TopCat.Presheaf.pushforwardEq_rfl /-
 @[simp]
 theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq (rfl : f = f) ℱ).Hom.app (op U) = 𝟙 _ :=
@@ -206,21 +221,26 @@ theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C)
   dsimp [pushforward_eq]
   simp
 #align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rfl
+-/
 
+#print TopCat.Presheaf.pushforwardEq_eq /-
 theorem pushforwardEq_eq {X Y : TopCat.{w}} {f g : X ⟶ Y} (h₁ h₂ : f = g) (ℱ : X.Presheaf C) :
     ℱ.pushforwardEq h₁ = ℱ.pushforwardEq h₂ :=
   rfl
 #align Top.presheaf.pushforward_eq_eq TopCat.Presheaf.pushforwardEq_eq
+-/
 
 namespace Pushforward
 
 variable {X : TopCat.{w}} (ℱ : X.Presheaf C)
 
+#print TopCat.Presheaf.Pushforward.id /-
 /-- The natural isomorphism between the pushforward of a presheaf along the identity continuous map
 and the original presheaf. -/
 def id : 𝟙 X _* ℱ ≅ ℱ :=
   isoWhiskerRight (NatIso.op (Opens.mapId X).symm) ℱ ≪≫ Functor.leftUnitor _
 #align Top.presheaf.pushforward.id TopCat.Presheaf.Pushforward.id
+-/
 
 #print TopCat.Presheaf.Pushforward.id_eq /-
 theorem id_eq : 𝟙 X _* ℱ = ℱ := by unfold pushforward_obj; rw [opens.map_id_eq];
@@ -228,13 +248,16 @@ theorem id_eq : 𝟙 X _* ℱ = ℱ := by unfold pushforward_obj; rw [opens.map_
 #align Top.presheaf.pushforward.id_eq TopCat.Presheaf.Pushforward.id_eq
 -/
 
+#print TopCat.Presheaf.Pushforward.id_hom_app' /-
 @[simp]
 theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
 #align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'
+-/
 
 attribute [local tidy] tactic.op_induction'
 
+#print TopCat.Presheaf.Pushforward.id_hom_app /-
 @[simp]
 theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) :=
   by
@@ -244,18 +267,23 @@ theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_
   rw [id_hom_app']
   congr
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app
+-/
 
+#print TopCat.Presheaf.Pushforward.id_inv_app' /-
 @[simp]
 theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
 #align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'
+-/
 
+#print TopCat.Presheaf.Pushforward.comp /-
 /-- The natural isomorphism between
 the pushforward of a presheaf along the composition of two continuous maps and
 the corresponding pushforward of a pushforward. -/
 def comp {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* ℱ ≅ g _* (f _* ℱ) :=
   isoWhiskerRight (NatIso.op (Opens.mapComp f g).symm) ℱ
 #align Top.presheaf.pushforward.comp TopCat.Presheaf.Pushforward.comp
+-/
 
 #print TopCat.Presheaf.Pushforward.comp_eq /-
 theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* ℱ = g _* (f _* ℱ) :=
@@ -263,18 +291,23 @@ theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* 
 #align Top.presheaf.pushforward.comp_eq TopCat.Presheaf.Pushforward.comp_eq
 -/
 
+#print TopCat.Presheaf.Pushforward.comp_hom_app /-
 @[simp]
 theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).Hom.app U = 𝟙 _ := by dsimp [comp]; tidy
 #align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_app
+-/
 
+#print TopCat.Presheaf.Pushforward.comp_inv_app /-
 @[simp]
 theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).inv.app U = 𝟙 _ := by dsimp [comp]; tidy
 #align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_app
+-/
 
 end Pushforward
 
+#print TopCat.Presheaf.pushforwardMap /-
 /-- A morphism of presheaves gives rise to a morphisms of the pushforwards of those presheaves.
 -/
 @[simps]
@@ -283,6 +316,7 @@ def pushforwardMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (
   app U := α.app _
   naturality' U V i := by erw [α.naturality]; rfl
 #align Top.presheaf.pushforward_map TopCat.Presheaf.pushforwardMap
+-/
 
 open CategoryTheory.Limits
 
@@ -292,6 +326,7 @@ variable [HasColimitsOfSize.{w, w} C]
 
 noncomputable section
 
+#print TopCat.Presheaf.pullbackObj /-
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf on `X`.
 
 This is defined in terms of left Kan extensions, which is just a fancy way of saying
@@ -301,13 +336,17 @@ This is defined in terms of left Kan extensions, which is just a fancy way of sa
 def pullbackObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
   (lan (Opens.map f).op).obj ℱ
 #align Top.presheaf.pullback_obj TopCat.Presheaf.pullbackObj
+-/
 
+#print TopCat.Presheaf.pullbackMap /-
 /-- Pulling back along continuous maps is functorial. -/
 def pullbackMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
     pullbackObj f ℱ ⟶ pullbackObj f 𝒢 :=
   (lan (Opens.map f).op).map α
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
+-/
 
+#print TopCat.Presheaf.pullbackObjObjOfImageOpen /-
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
 def pullbackObjObjOfImageOpen {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
@@ -330,11 +369,13 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf
     is_colimit.cocone_point_unique_up_to_iso (colimit.is_colimit _)
       (colimit_of_diagram_terminal hx _)
 #align Top.presheaf.pullback_obj_obj_of_image_open TopCat.Presheaf.pullbackObjObjOfImageOpen
+-/
 
 namespace Pullback
 
 variable {X Y : TopCat.{w}} (ℱ : Y.Presheaf C)
 
+#print TopCat.Presheaf.Pullback.id /-
 /-- The pullback along the identity is isomorphic to the original presheaf. -/
 def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
   NatIso.ofComponents
@@ -348,7 +389,9 @@ def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
     erw [colimit.ι_desc_assoc]
     dsimp; simp only [← ℱ.map_comp]; congr
 #align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.id
+-/
 
+#print TopCat.Presheaf.Pullback.id_inv_app /-
 theorem id_inv_app (U : Opens Y) :
     (id ℱ).inv.app (op U) =
       colimit.ι (Lan.diagram (Opens.map (𝟙 Y)).op ℱ (op U))
@@ -360,6 +403,7 @@ theorem id_inv_app (U : Opens Y) :
   dsimp
   rw [← ℱ.map_comp, ← ℱ.map_id]; rfl
 #align Top.presheaf.pullback.id_inv_app TopCat.Presheaf.Pullback.id_inv_app
+-/
 
 end Pullback
 
@@ -367,6 +411,7 @@ end Pullback
 
 variable (C)
 
+#print TopCat.Presheaf.pushforward /-
 /-- The pushforward functor.
 -/
 def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
@@ -374,13 +419,17 @@ def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
   obj := pushforwardObj f
   map := @pushforwardMap _ _ X Y f
 #align Top.presheaf.pushforward TopCat.Presheaf.pushforward
+-/
 
+#print TopCat.Presheaf.pushforward_map_app' /-
 @[simp]
 theorem pushforward_map_app' {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (α : ℱ ⟶ 𝒢)
     {U : (Opens Y)ᵒᵖ} : ((pushforward C f).map α).app U = α.app (op <| (Opens.map f).obj U.unop) :=
   rfl
 #align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'
+-/
 
+#print TopCat.Presheaf.id_pushforward /-
 theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presheaf C) :=
   by
   apply CategoryTheory.Functor.ext
@@ -390,17 +439,21 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
     simpa [eq_to_hom_map]
   · intros; apply pushforward.id_eq
 #align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforward
+-/
 
 section Iso
 
+#print TopCat.Presheaf.presheafEquivOfIso /-
 /-- A homeomorphism of spaces gives an equivalence of categories of presheaves. -/
 @[simps]
 def presheafEquivOfIso {X Y : TopCat} (H : X ≅ Y) : X.Presheaf C ≌ Y.Presheaf C :=
   Equivalence.congrLeft (Opens.mapMapIso H).symm.op
 #align Top.presheaf.presheaf_equiv_of_iso TopCat.Presheaf.presheafEquivOfIso
+-/
 
 variable {C}
 
+#print TopCat.Presheaf.toPushforwardOfIso /-
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -408,7 +461,9 @@ def toPushforwardOfIso {X Y : TopCat} (H : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 :
     (α : H.Hom _* ℱ ⟶ 𝒢) : ℱ ⟶ H.inv _* 𝒢 :=
   (presheafEquivOfIso _ H).toAdjunction.homEquiv ℱ 𝒢 α
 #align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIso
+-/
 
+#print TopCat.Presheaf.toPushforwardOfIso_app /-
 @[simp]
 theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 : Y.Presheaf C}
     (H₂ : H₁.Hom _* ℱ ⟶ 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -423,7 +478,9 @@ theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf
     presheaf_equiv_of_iso_inverse_map_app, adjunction.mk_of_unit_counit_hom_equiv_apply]
   congr
 #align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_app
+-/
 
+#print TopCat.Presheaf.pushforwardToOfIso /-
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -431,7 +488,9 @@ def pushforwardToOfIso {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {
     (H₂ : ℱ ⟶ H₁.Hom _* 𝒢) : H₁.inv _* ℱ ⟶ 𝒢 :=
   ((presheafEquivOfIso _ H₁.symm).toAdjunction.homEquiv ℱ 𝒢).symm H₂
 #align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIso
+-/
 
+#print TopCat.Presheaf.pushforwardToOfIso_app /-
 @[simp]
 theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {𝒢 : X.Presheaf C}
     (H₂ : ℱ ⟶ H₁.Hom _* 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -440,43 +499,54 @@ theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf
         𝒢.map (eqToHom (by simp [opens.map, Set.preimage_preimage])) :=
   by simpa [pushforward_to_of_iso, equivalence.to_adjunction]
 #align Top.presheaf.pushforward_to_of_iso_app TopCat.Presheaf.pushforwardToOfIso_app
+-/
 
 end Iso
 
 variable (C) [HasColimitsOfSize.{w, w} C]
 
+#print TopCat.Presheaf.pullback /-
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `X`. -/
 @[simps map_app]
 def pullback {X Y : TopCat.{w}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
   lan (Opens.map f).op
 #align Top.presheaf.pullback TopCat.Presheaf.pullback
+-/
 
+#print TopCat.Presheaf.pullbackObj_eq_pullbackObj /-
 @[simp]
 theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCat.{w}} (f : X ⟶ Y)
     (ℱ : Y.Presheaf C) : (pullback C f).obj ℱ = pullbackObj f ℱ :=
   rfl
 #align Top.presheaf.pullback_obj_eq_pullback_obj TopCat.Presheaf.pullbackObj_eq_pullbackObj
+-/
 
+#print TopCat.Presheaf.pushforwardPullbackAdjunction /-
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
 def pushforwardPullbackAdjunction {X Y : TopCat.{w}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
+-/
 
+#print TopCat.Presheaf.pullbackHomIsoPushforwardInv /-
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/
 def pullbackHomIsoPushforwardInv {X Y : TopCat.{w}} (H : X ≅ Y) :
     pullback C H.Hom ≅ pushforward C H.inv :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.Hom)
     (presheafEquivOfIso C H.symm).toAdjunction
 #align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInv
+-/
 
+#print TopCat.Presheaf.pullbackInvIsoPushforwardHom /-
 /-- Pulling back along the inverse of a homeomorphism is the same as pushing forward along it. -/
 def pullbackInvIsoPushforwardHom {X Y : TopCat.{w}} (H : X ≅ Y) :
     pullback C H.inv ≅ pushforward C H.Hom :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.inv)
     (presheafEquivOfIso C H).toAdjunction
 #align Top.presheaf.pullback_inv_iso_pushforward_hom TopCat.Presheaf.pullbackInvIsoPushforwardHom
+-/
 
 end Presheaf
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -81,7 +81,7 @@ unsafe def restrict_attr : user_attribute (tactic Unit → tactic Unit) Unit
       dependencies := [] }
 #align Top.presheaf.restrict_attr Top.presheaf.restrict_attr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 /-- A tactic to discharge goals of type `U ≤ V` for `Top.presheaf.restrict_open` -/
 unsafe def restrict_tac : ∀ n : ℕ, tactic Unit
   | 0 => tactic.fail "`restrict_tac` failed"

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
+! leanprover-community/mathlib commit 13361559d66b84f80b6d5a1c4a26aa5054766725
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -288,31 +288,29 @@ open CategoryTheory.Limits
 
 section Pullback
 
-variable [HasColimits C]
+variable [HasColimitsOfSize.{w, w} C]
 
 noncomputable section
 
-#print TopCat.Presheaf.pullbackObj /-
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf on `X`.
 
 This is defined in terms of left Kan extensions, which is just a fancy way of saying
 "take the colimits over the open sets whose preimage contains U".
 -/
 @[simps]
-def pullbackObj {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
+def pullbackObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
   (lan (Opens.map f).op).obj ℱ
 #align Top.presheaf.pullback_obj TopCat.Presheaf.pullbackObj
--/
 
 /-- Pulling back along continuous maps is functorial. -/
-def pullbackMap {X Y : TopCat.{v}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
+def pullbackMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
     pullbackObj f ℱ ⟶ pullbackObj f 𝒢 :=
   (lan (Opens.map f).op).map α
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
 
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
-def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
+def pullbackObjObjOfImageOpen {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
     (H : IsOpen (f '' U)) : (pullbackObj f ℱ).obj (op U) ≅ ℱ.obj (op ⟨_, H⟩) :=
   by
   let x : costructured_arrow (opens.map f).op (op U) :=
@@ -335,7 +333,7 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
 
 namespace Pullback
 
-variable {X Y : TopCat.{v}} (ℱ : Y.Presheaf C)
+variable {X Y : TopCat.{w}} (ℱ : Y.Presheaf C)
 
 /-- The pullback along the identity is isomorphic to the original presheaf. -/
 def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
@@ -445,12 +443,12 @@ theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf
 
 end Iso
 
-variable (C) [HasColimits C]
+variable (C) [HasColimitsOfSize.{w, w} C]
 
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `X`. -/
 @[simps map_app]
-def pullback {X Y : TopCat.{v}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
+def pullback {X Y : TopCat.{w}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
   lan (Opens.map f).op
 #align Top.presheaf.pullback TopCat.Presheaf.pullback
 
@@ -462,19 +460,19 @@ theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCa
 
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
-def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
+def pushforwardPullbackAdjunction {X Y : TopCat.{w}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
 
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/
-def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
+def pullbackHomIsoPushforwardInv {X Y : TopCat.{w}} (H : X ≅ Y) :
     pullback C H.Hom ≅ pushforward C H.inv :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.Hom)
     (presheafEquivOfIso C H.symm).toAdjunction
 #align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInv
 
 /-- Pulling back along the inverse of a homeomorphism is the same as pushing forward along it. -/
-def pullbackInvIsoPushforwardHom {X Y : TopCat.{v}} (H : X ≅ Y) :
+def pullbackInvIsoPushforwardHom {X Y : TopCat.{w}} (H : X ≅ Y) :
     pullback C H.inv ≅ pushforward C H.Hom :=
   Adjunction.leftAdjointUniq (pushforwardPullbackAdjunction C H.inv)
     (presheafEquivOfIso C H).toAdjunction

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

@@ -51,7 +51,8 @@ namespace TopCat
 /-- The category of `C`-valued presheaves on a (bundled) topological space `X`. -/
 @[nolint has_nonempty_instance]
 def Presheaf (X : TopCat.{w}) : Type max u v w :=
-  (Opens X)ᵒᵖ ⥤ C deriving Category
+  (Opens X)ᵒᵖ ⥤ C
+deriving Category
 #align Top.presheaf TopCat.Presheaf
 -/
 
@@ -389,7 +390,7 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
     ext U
     have h := f.congr; erw [h (opens.op_map_id_obj U)]
     simpa [eq_to_hom_map]
-  · intros ; apply pushforward.id_eq
+  · intros; apply pushforward.id_eq
 #align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforward
 
 section Iso

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

@@ -101,9 +101,6 @@ example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓
   run_tac
     restrict_tac'
 
-/- warning: Top.presheaf.restrict -> TopCat.Presheaf.restrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict TopCat.Presheaf.restrictₓ'. -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
 and the notation `x |_ₗ U ⟪i⟫` (`l` stands for `le`) for `i : U ≤ V`.
@@ -121,9 +118,6 @@ scoped[AlgebraicGeometry]
   notation:80 x " |_ₗ " U " ⟪" e "⟫ " =>
     @TopCat.Presheaf.restrict _ _ _ _ _ _ x U (@homOfLE (Opens _) _ U _ e)
 
-/- warning: Top.presheaf.restrict_open -> TopCat.Presheaf.restrictOpen is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_open TopCat.Presheaf.restrictOpenₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ U`, where the proof `U ≤ V` is inferred by
@@ -140,9 +134,6 @@ abbrev restrictOpen {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
 -- mathport name: «expr |_ »
 scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
-/- warning: Top.presheaf.restrict_restrict -> TopCat.Presheaf.restrict_restrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrictₓ'. -/
 @[simp]
 theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
@@ -150,9 +141,6 @@ theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCatego
   rfl
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
 
-/- warning: Top.presheaf.map_restrict -> TopCat.Presheaf.map_restrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.map_restrict TopCat.Presheaf.map_restrictₓ'. -/
 @[simp]
 theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
@@ -171,30 +159,18 @@ def pushforwardObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) : Y.Pre
 -- mathport name: «expr _* »
 infixl:80 " _* " => pushforwardObj
 
-/- warning: Top.presheaf.pushforward_obj_obj -> TopCat.Presheaf.pushforwardObj_obj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_objₓ'. -/
 @[simp]
 theorem pushforwardObj_obj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U : (Opens Y)ᵒᵖ) :
     (f _* ℱ).obj U = ℱ.obj ((Opens.map f).op.obj U) :=
   rfl
 #align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_obj
 
-/- warning: Top.presheaf.pushforward_obj_map -> TopCat.Presheaf.pushforwardObj_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_mapₓ'. -/
 @[simp]
 theorem pushforwardObj_map {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) {U V : (Opens Y)ᵒᵖ}
     (i : U ⟶ V) : (f _* ℱ).map i = ℱ.map ((Opens.map f).op.map i) :=
   rfl
 #align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_map
 
-/- warning: Top.presheaf.pushforward_eq -> TopCat.Presheaf.pushforwardEq is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y}, (Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) -> (forall (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y}, (Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) -> (forall (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq TopCat.Presheaf.pushforwardEqₓ'. -/
 /--
 An equality of continuous maps induces a natural isomorphism between the pushforwards of a presheaf
 along those maps.
@@ -210,9 +186,6 @@ theorem pushforward_eq' {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.
 #align Top.presheaf.pushforward_eq' TopCat.Presheaf.pushforward_eq'
 -/
 
-/- warning: Top.presheaf.pushforward_eq_hom_app -> TopCat.Presheaf.pushforwardEq_hom_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_appₓ'. -/
 @[simp]
 theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq h ℱ).Hom.app U =
@@ -220,17 +193,11 @@ theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (
   by simp [pushforward_eq]
 #align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_app
 
-/- warning: Top.presheaf.pushforward_eq'_hom_app -> TopCat.Presheaf.pushforward_eq'_hom_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_appₓ'. -/
 theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C)
     (U) : NatTrans.app (eqToHom (pushforward_eq' h ℱ)) U = ℱ.map (eqToHom (by rw [h])) := by
   simpa [eq_to_hom_map]
 #align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_app
 
-/- warning: Top.presheaf.pushforward_eq_rfl -> TopCat.Presheaf.pushforwardEq_rfl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rflₓ'. -/
 @[simp]
 theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq (rfl : f = f) ℱ).Hom.app (op U) = 𝟙 _ :=
@@ -239,12 +206,6 @@ theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C)
   simp
 #align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rfl
 
-/- warning: Top.presheaf.pushforward_eq_eq -> TopCat.Presheaf.pushforwardEq_eq is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h₁ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (h₂ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), Eq.{succ (max u1 u2)} (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₁ ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₂ ℱ)
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h₁ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (h₂ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), Eq.{max (succ u2) (succ u1)} (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₁ ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₂ ℱ)
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_eq TopCat.Presheaf.pushforwardEq_eqₓ'. -/
 theorem pushforwardEq_eq {X Y : TopCat.{w}} {f g : X ⟶ Y} (h₁ h₂ : f = g) (ℱ : X.Presheaf C) :
     ℱ.pushforwardEq h₁ = ℱ.pushforwardEq h₂ :=
   rfl
@@ -254,12 +215,6 @@ namespace Pushforward
 
 variable {X : TopCat.{w}} (ℱ : X.Presheaf C)
 
-/- warning: Top.presheaf.pushforward.id -> TopCat.Presheaf.Pushforward.id is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id TopCat.Presheaf.Pushforward.idₓ'. -/
 /-- The natural isomorphism between the pushforward of a presheaf along the identity continuous map
 and the original presheaf. -/
 def id : 𝟙 X _* ℱ ≅ ℱ :=
@@ -272,9 +227,6 @@ theorem id_eq : 𝟙 X _* ℱ = ℱ := by unfold pushforward_obj; rw [opens.map_
 #align Top.presheaf.pushforward.id_eq TopCat.Presheaf.Pushforward.id_eq
 -/
 
-/- warning: Top.presheaf.pushforward.id_hom_app' -> TopCat.Presheaf.Pushforward.id_hom_app' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'ₓ'. -/
 @[simp]
 theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
@@ -282,9 +234,6 @@ theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (
 
 attribute [local tidy] tactic.op_induction'
 
-/- warning: Top.presheaf.pushforward.id_hom_app -> TopCat.Presheaf.Pushforward.id_hom_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_appₓ'. -/
 @[simp]
 theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) :=
   by
@@ -295,20 +244,11 @@ theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_
   congr
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app
 
-/- warning: Top.presheaf.pushforward.id_inv_app' -> TopCat.Presheaf.Pushforward.id_inv_app' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'ₓ'. -/
 @[simp]
 theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
 #align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'
 
-/- warning: Top.presheaf.pushforward.comp -> TopCat.Presheaf.Pushforward.comp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp TopCat.Presheaf.Pushforward.compₓ'. -/
 /-- The natural isomorphism between
 the pushforward of a presheaf along the composition of two continuous maps and
 the corresponding pushforward of a pushforward. -/
@@ -322,17 +262,11 @@ theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* 
 #align Top.presheaf.pushforward.comp_eq TopCat.Presheaf.Pushforward.comp_eq
 -/
 
-/- warning: Top.presheaf.pushforward.comp_hom_app -> TopCat.Presheaf.Pushforward.comp_hom_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_appₓ'. -/
 @[simp]
 theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).Hom.app U = 𝟙 _ := by dsimp [comp]; tidy
 #align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_app
 
-/- warning: Top.presheaf.pushforward.comp_inv_app -> TopCat.Presheaf.Pushforward.comp_inv_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_appₓ'. -/
 @[simp]
 theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).inv.app U = 𝟙 _ := by dsimp [comp]; tidy
@@ -340,12 +274,6 @@ theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
 
 end Pushforward
 
-/- warning: Top.presheaf.pushforward_map -> TopCat.Presheaf.pushforwardMap is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))) ℱ 𝒢) -> (Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f 𝒢))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) ℱ 𝒢) -> (Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f 𝒢))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_map TopCat.Presheaf.pushforwardMapₓ'. -/
 /-- A morphism of presheaves gives rise to a morphisms of the pushforwards of those presheaves.
 -/
 @[simps]
@@ -375,21 +303,12 @@ def pullbackObj {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Preshe
 #align Top.presheaf.pullback_obj TopCat.Presheaf.pullbackObj
 -/
 
-/- warning: Top.presheaf.pullback_map -> TopCat.Presheaf.pullbackMap is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y))) ℱ 𝒢) -> (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1))) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f 𝒢))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y))) ℱ 𝒢) -> (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X))) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f 𝒢))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMapₓ'. -/
 /-- Pulling back along continuous maps is functorial. -/
 def pullbackMap {X Y : TopCat.{v}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
     pullbackObj f ℱ ⟶ pullbackObj f 𝒢 :=
   (lan (Opens.map f).op).map α
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
 
-/- warning: Top.presheaf.pullback_obj_obj_of_image_open -> TopCat.Presheaf.pullbackObjObjOfImageOpen is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_obj_obj_of_image_open TopCat.Presheaf.pullbackObjObjOfImageOpenₓ'. -/
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
 def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
@@ -417,12 +336,6 @@ namespace Pullback
 
 variable {X Y : TopCat.{v}} (ℱ : Y.Presheaf C)
 
-/- warning: Top.presheaf.pullback.id -> TopCat.Presheaf.Pullback.id is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y), CategoryTheory.Iso.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) ℱ
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y), CategoryTheory.Iso.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) ℱ
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.idₓ'. -/
 /-- The pullback along the identity is isomorphic to the original presheaf. -/
 def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
   NatIso.ofComponents
@@ -437,9 +350,6 @@ def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
     dsimp; simp only [← ℱ.map_comp]; congr
 #align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.id
 
-/- warning: Top.presheaf.pullback.id_inv_app -> TopCat.Presheaf.Pullback.id_inv_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback.id_inv_app TopCat.Presheaf.Pullback.id_inv_appₓ'. -/
 theorem id_inv_app (U : Opens Y) :
     (id ℱ).inv.app (op U) =
       colimit.ι (Lan.diagram (Opens.map (𝟙 Y)).op ℱ (op U))
@@ -458,12 +368,6 @@ end Pullback
 
 variable (C)
 
-/- warning: Top.presheaf.pushforward -> TopCat.Presheaf.pushforward is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y))
-but is expected to have type
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward TopCat.Presheaf.pushforwardₓ'. -/
 /-- The pushforward functor.
 -/
 def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
@@ -472,21 +376,12 @@ def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
   map := @pushforwardMap _ _ X Y f
 #align Top.presheaf.pushforward TopCat.Presheaf.pushforward
 
-/- warning: Top.presheaf.pushforward_map_app' -> TopCat.Presheaf.pushforward_map_app' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'ₓ'. -/
 @[simp]
 theorem pushforward_map_app' {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (α : ℱ ⟶ 𝒢)
     {U : (Opens Y)ᵒᵖ} : ((pushforward C f).map α).app U = α.app (op <| (Opens.map f).obj U.unop) :=
   rfl
 #align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'
 
-/- warning: Top.presheaf.id_pushforward -> TopCat.Presheaf.id_pushforward is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}}, Eq.{succ (max (max u1 u2) u3 u2 u1)} (CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X)) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X)) (CategoryTheory.Functor.id.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))
-but is expected to have type
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}}, Eq.{max (max (succ u3) (succ u2)) (succ u1)} (CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X)) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)) (CategoryTheory.Functor.id.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforwardₓ'. -/
 theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presheaf C) :=
   by
   apply CategoryTheory.Functor.ext
@@ -499,12 +394,6 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
 
 section Iso
 
-/- warning: Top.presheaf.presheaf_equiv_of_iso -> TopCat.Presheaf.presheafEquivOfIso is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}}, (CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) -> (CategoryTheory.Equivalence.{max u3 u1, max u3 u1, max u2 u1 u3, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X) (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}}, (CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) -> (CategoryTheory.Equivalence.{max u1 u3, max u1 u3, max (max u2 u1) u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.presheaf_equiv_of_iso TopCat.Presheaf.presheafEquivOfIsoₓ'. -/
 /-- A homeomorphism of spaces gives an equivalence of categories of presheaves. -/
 @[simps]
 def presheafEquivOfIso {X Y : TopCat} (H : X ≅ Y) : X.Presheaf C ≌ Y.Presheaf C :=
@@ -513,12 +402,6 @@ def presheafEquivOfIso {X Y : TopCat} (H : X ≅ Y) : X.Presheaf C ≌ Y.Preshea
 
 variable {C}
 
-/- warning: Top.presheaf.to_pushforward_of_iso -> TopCat.Presheaf.toPushforwardOfIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H) ℱ) 𝒢) -> (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H) 𝒢))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H) ℱ) 𝒢) -> (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H) 𝒢))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIsoₓ'. -/
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -527,9 +410,6 @@ def toPushforwardOfIso {X Y : TopCat} (H : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 :
   (presheafEquivOfIso _ H).toAdjunction.homEquiv ℱ 𝒢 α
 #align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIso
 
-/- warning: Top.presheaf.to_pushforward_of_iso_app -> TopCat.Presheaf.toPushforwardOfIso_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_appₓ'. -/
 @[simp]
 theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 : Y.Presheaf C}
     (H₂ : H₁.Hom _* ℱ ⟶ 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -545,12 +425,6 @@ theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf
   congr
 #align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_app
 
-/- warning: Top.presheaf.pushforward_to_of_iso -> TopCat.Presheaf.pushforwardToOfIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X}, (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢)) -> (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢)
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H₁) 𝒢)) -> (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H₁) ℱ) 𝒢)
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIsoₓ'. -/
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -559,9 +433,6 @@ def pushforwardToOfIso {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {
   ((presheafEquivOfIso _ H₁.symm).toAdjunction.homEquiv ℱ 𝒢).symm H₂
 #align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIso
 
-/- warning: Top.presheaf.pushforward_to_of_iso_app -> TopCat.Presheaf.pushforwardToOfIso_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_to_of_iso_app TopCat.Presheaf.pushforwardToOfIso_appₓ'. -/
 @[simp]
 theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {𝒢 : X.Presheaf C}
     (H₂ : ℱ ⟶ H₁.Hom _* 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -575,12 +446,6 @@ end Iso
 
 variable (C) [HasColimits C]
 
-/- warning: Top.presheaf.pullback -> TopCat.Presheaf.pullback is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback TopCat.Presheaf.pullbackₓ'. -/
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `X`. -/
 @[simps map_app]
@@ -588,36 +453,18 @@ def pullback {X Y : TopCat.{v}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
   lan (Opens.map f).op
 #align Top.presheaf.pullback TopCat.Presheaf.pullback
 
-/- warning: Top.presheaf.pullback_obj_eq_pullback_obj -> TopCat.Presheaf.pullbackObj_eq_pullbackObj is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_3 : CategoryTheory.Category.{u1, u2} C] [_inst_4 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_3] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_3 Y), Eq.{succ (max u2 u1)} (TopCat.Presheaf.{u1, u1, u2} C _inst_3 X) (CategoryTheory.Functor.obj.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_3 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_3 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_3 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_3 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_3 _inst_4 X Y f) ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_3 _inst_4 X Y f ℱ)
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_3 : CategoryTheory.Category.{u2, u1} C] [_inst_4 : CategoryTheory.Limits.HasColimits.{u2, u1} C _inst_3] {X : TopCat.{u2}} {Y : TopCat.{u2}} (f : Quiver.Hom.{succ u2, succ u2} TopCat.{u2} (CategoryTheory.CategoryStruct.toQuiver.{u2, succ u2} TopCat.{u2} (CategoryTheory.Category.toCategoryStruct.{u2, succ u2} TopCat.{u2} instTopCatLargeCategory.{u2})) X Y) (ℱ : TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y), Eq.{max (succ u2) (succ u1)} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (Prefunctor.obj.{succ u2, succ u2, max u2 u1, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 Y))) (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 X))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u2 u1, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 X) (TopCat.Presheaf.pullback.{u2, u1} C _inst_3 _inst_4 X Y f)) ℱ) (TopCat.Presheaf.pullbackObj.{u2, u1} C _inst_3 _inst_4 X Y f ℱ)
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_obj_eq_pullback_obj TopCat.Presheaf.pullbackObj_eq_pullbackObjₓ'. -/
 @[simp]
 theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCat.{w}} (f : X ⟶ Y)
     (ℱ : Y.Presheaf C) : (pullback C f).obj ℱ = pullbackObj f ℱ :=
   rfl
 #align Top.presheaf.pullback_obj_eq_pullback_obj TopCat.Presheaf.pullbackObj_eq_pullbackObj
 
-/- warning: Top.presheaf.pushforward_pullback_adjunction -> TopCat.Presheaf.pushforwardPullbackAdjunction is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y), CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y f) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y f)
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y), CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y f) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y f)
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunctionₓ'. -/
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
 def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
 
-/- warning: Top.presheaf.pullback_hom_iso_pushforward_inv -> TopCat.Presheaf.pullbackHomIsoPushforwardInv is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInvₓ'. -/
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/
 def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.Hom ≅ pushforward C H.inv :=
@@ -625,12 +472,6 @@ def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
     (presheafEquivOfIso C H.symm).toAdjunction
 #align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInv
 
-/- warning: Top.presheaf.pullback_inv_iso_pushforward_hom -> TopCat.Presheaf.pullbackInvIsoPushforwardHom is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H))
-but is expected to have type
-  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_inv_iso_pushforward_hom TopCat.Presheaf.pullbackInvIsoPushforwardHomₓ'. -/
 /-- Pulling back along the inverse of a homeomorphism is the same as pushing forward along it. -/
 def pullbackInvIsoPushforwardHom {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.inv ≅ pushforward C H.Hom :=

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

@@ -146,9 +146,7 @@ Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_
 @[simp]
 theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
-    x |_ V |_ U = x |_ U := by
-  delta restrict_open restrict
-  rw [← comp_apply, ← functor.map_comp]
+    x |_ V |_ U = x |_ U := by delta restrict_open restrict; rw [← comp_apply, ← functor.map_comp];
   rfl
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
 
@@ -158,9 +156,7 @@ Case conversion may be inaccurate. Consider using '#align Top.presheaf.map_restr
 @[simp]
 theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
-    e.app _ (x |_ U) = e.app _ x |_ U :=
-  by
-  delta restrict_open restrict
+    e.app _ (x |_ U) = e.app _ x |_ U := by delta restrict_open restrict;
   rw [← comp_apply, nat_trans.naturality, comp_apply]
 #align Top.presheaf.map_restrict TopCat.Presheaf.map_restrict
 
@@ -271,9 +267,7 @@ def id : 𝟙 X _* ℱ ≅ ℱ :=
 #align Top.presheaf.pushforward.id TopCat.Presheaf.Pushforward.id
 
 #print TopCat.Presheaf.Pushforward.id_eq /-
-theorem id_eq : 𝟙 X _* ℱ = ℱ := by
-  unfold pushforward_obj
-  rw [opens.map_id_eq]
+theorem id_eq : 𝟙 X _* ℱ = ℱ := by unfold pushforward_obj; rw [opens.map_id_eq];
   erw [functor.id_comp]
 #align Top.presheaf.pushforward.id_eq TopCat.Presheaf.Pushforward.id_eq
 -/
@@ -282,9 +276,7 @@ theorem id_eq : 𝟙 X _* ℱ = ℱ := by
 <too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'ₓ'. -/
 @[simp]
-theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
-  by
-  dsimp [id]
+theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
 #align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'
 
@@ -307,9 +299,7 @@ theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_
 <too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'ₓ'. -/
 @[simp]
-theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
-  by
-  dsimp [id]
+theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by dsimp [id];
   simp
 #align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'
 
@@ -337,9 +327,7 @@ theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* 
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_appₓ'. -/
 @[simp]
 theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
-    (comp ℱ f g).Hom.app U = 𝟙 _ := by
-  dsimp [comp]
-  tidy
+    (comp ℱ f g).Hom.app U = 𝟙 _ := by dsimp [comp]; tidy
 #align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_app
 
 /- warning: Top.presheaf.pushforward.comp_inv_app -> TopCat.Presheaf.Pushforward.comp_inv_app is a dubious translation:
@@ -347,9 +335,7 @@ theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_appₓ'. -/
 @[simp]
 theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
-    (comp ℱ f g).inv.app U = 𝟙 _ := by
-  dsimp [comp]
-  tidy
+    (comp ℱ f g).inv.app U = 𝟙 _ := by dsimp [comp]; tidy
 #align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_app
 
 end Pushforward
@@ -366,9 +352,7 @@ Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforwa
 def pushforwardMap {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (α : ℱ ⟶ 𝒢) : f _* ℱ ⟶ f _* 𝒢
     where
   app U := α.app _
-  naturality' U V i := by
-    erw [α.naturality]
-    rfl
+  naturality' U V i := by erw [α.naturality]; rfl
 #align Top.presheaf.pushforward_map TopCat.Presheaf.pushforwardMap
 
 open CategoryTheory.Limits
@@ -508,11 +492,9 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
   apply CategoryTheory.Functor.ext
   · intros
     ext U
-    have h := f.congr
-    erw [h (opens.op_map_id_obj U)]
+    have h := f.congr; erw [h (opens.op_map_id_obj U)]
     simpa [eq_to_hom_map]
-  · intros
-    apply pushforward.id_eq
+  · intros ; apply pushforward.id_eq
 #align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforward
 
 section Iso

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

@@ -102,10 +102,7 @@ example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓
     restrict_tac'
 
 /- warning: Top.presheaf.restrict -> TopCat.Presheaf.restrict is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (forall {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))))) U V) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))))
-but is expected to have type
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) V))) -> (forall {U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) U V) -> (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict TopCat.Presheaf.restrictₓ'. -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
@@ -125,10 +122,7 @@ scoped[AlgebraicGeometry]
     @TopCat.Presheaf.restrict _ _ _ _ _ _ x U (@homOfLE (Opens _) _ U _ e)
 
 /- warning: Top.presheaf.restrict_open -> TopCat.Presheaf.restrictOpen is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (forall (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)), (autoParamₓ.{0} (LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 39 (OfNat.mk.{0} Nat 39 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 112 (OfNat.mk.{0} Nat 112 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 104 (OfNat.mk.{0} Nat 104 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 84 (OfNat.mk.{0} Nat 84 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 112 (OfNat.mk.{0} Nat 112 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous)))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))))
-but is expected to have type
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) V))) -> (forall (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)), (autoParam.{0} (LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) U V) _auto._@.Mathlib.Topology.Sheaves.Presheaf._hyg.1775) -> (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_open TopCat.Presheaf.restrictOpenₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
 /-- The restriction of a section along an inclusion of open sets.
@@ -147,10 +141,7 @@ abbrev restrictOpen {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
 scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
 /- warning: Top.presheaf.restrict_restrict -> TopCat.Presheaf.restrict_restrict is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {W : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} (e₁ : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (e₂ : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) V W) (x : coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) W))), Eq.{succ u4} (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F V (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F W x V e₂) U e₁) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F W x U (le_trans.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)))) U V W e₁ e₂))
-but is expected to have type
-  forall {X : TopCat.{u4}} {C : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u2, u3} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_2] {F : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} {U : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {V : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {W : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} (e₁ : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) U V) (e₂ : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) V W) (x : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W))), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F V (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F W x V (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W a)) (e₂ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a) a_1))))))) U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (e₁ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1))))))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F W x U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W a)) (e₂ a (Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (e₁ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrictₓ'. -/
 @[simp]
 theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
@@ -162,10 +153,7 @@ theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCatego
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
 
 /- warning: Top.presheaf.map_restrict -> TopCat.Presheaf.map_restrict is a dubious translation:
-lean 3 declaration is
-  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {G : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} (e : Quiver.Hom.{succ (max u1 u3), max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (TopCat.Presheaf.category.{u3, u1, u2} C _inst_2 X))) F G) {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} (h : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (x : coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))), Eq.{succ u4} (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (coeFn.{succ u3, succ u4} (Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (fun (f : Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) => (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u3, u4} C _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (CategoryTheory.NatTrans.app.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F G e (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F V x U h)) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 G V (coeFn.{succ u3, succ u4} (Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) (fun (f : Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) => (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u3, u4} C _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) (CategoryTheory.NatTrans.app.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F G e (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) x) U h)
-but is expected to have type
-  forall {X : TopCat.{u4}} {C : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u2, u3} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_2] {F : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} {G : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} (e : Quiver.Hom.{max (succ u2) (succ u4), max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (TopCat.instCategoryPresheaf.{u4, u2, u3} C _inst_2 X))) F G) {U : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {V : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} (h : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) U V) (x : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V))), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U))) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (CategoryTheory.NatTrans.app.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F G e (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F V x U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (h a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 G V (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (CategoryTheory.NatTrans.app.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F G e (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) x) U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (h a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.map_restrict TopCat.Presheaf.map_restrictₓ'. -/
 @[simp]
 theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
@@ -188,10 +176,7 @@ def pushforwardObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) : Y.Pre
 infixl:80 " _* " => pushforwardObj
 
 /- warning: Top.presheaf.pushforward_obj_obj -> TopCat.Presheaf.pushforwardObj_obj is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u3} C (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u3} C (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_objₓ'. -/
 @[simp]
 theorem pushforwardObj_obj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U : (Opens Y)ᵒᵖ) :
@@ -200,10 +185,7 @@ theorem pushforwardObj_obj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C)
 #align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_obj
 
 /- warning: Top.presheaf.pushforward_obj_map -> TopCat.Presheaf.pushforwardObj_map is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))} {V : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))} (i : Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (Quiver.opposite.{u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))))) U V), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) V)) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U V i) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) V) (CategoryTheory.Functor.map.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U V i))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))} {V : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))} (i : Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Quiver.opposite.{u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) U V), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) V)) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U V i) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) V) (Prefunctor.map.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U V i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_mapₓ'. -/
 @[simp]
 theorem pushforwardObj_map {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) {U V : (Opens Y)ᵒᵖ}
@@ -233,10 +215,7 @@ theorem pushforward_eq' {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.
 -/
 
 /- warning: Top.presheaf.pushforward_eq_hom_app -> TopCat.Presheaf.pushforwardEq_hom_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (id.{succ u1} (Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Quiver.Hom.op.{u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.eqToHom.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.mpr.{0} (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y _a) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) (rfl.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) g h)) (rfl.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))))))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (id.{succ u1} (Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Quiver.Hom.op.{u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.eqToHom.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.mpr.{0} (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (id.{0} (Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y _a)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) (Eq.refl.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) g h)) (Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_appₓ'. -/
 @[simp]
 theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) (U) :
@@ -246,10 +225,7 @@ theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (
 #align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_app
 
 /- warning: Top.presheaf.pushforward_eq'_hom_app -> TopCat.Presheaf.pushforward_eq'_hom_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.eqToHom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforward_eq'.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y _a)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) (rfl.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) g h)) (rfl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.eqToHom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforward_eq'.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (id.{0} (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y _a))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) (Eq.refl.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) g h)) (Eq.refl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_appₓ'. -/
 theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C)
     (U) : NatTrans.app (eqToHom (pushforward_eq' h ℱ)) U = ℱ.map (eqToHom (by rw [h])) := by
@@ -257,10 +233,7 @@ theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (
 #align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_app
 
 /- warning: Top.presheaf.pushforward_eq_rfl -> TopCat.Presheaf.pushforwardEq_rfl is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f f (rfl.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f f (rfl.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rflₓ'. -/
 @[simp]
 theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U) :
@@ -306,10 +279,7 @@ theorem id_eq : 𝟙 X _* ℱ = ℱ := by
 -/
 
 /- warning: Top.presheaf.pushforward.id_hom_app' -> TopCat.Presheaf.Pushforward.id_hom_app' is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)) (p : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (p : IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'ₓ'. -/
 @[simp]
 theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
@@ -321,10 +291,7 @@ theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (
 attribute [local tidy] tactic.op_induction'
 
 /- warning: Top.presheaf.pushforward.id_hom_app -> TopCat.Presheaf.Pushforward.id_hom_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) U) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) U) U (TopologicalSpace.Opens.op_map_id_obj.{u1} X U)))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)))) U) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)))) U) U (TopologicalSpace.Opens.op_map_id_obj.{u1} X U)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_appₓ'. -/
 @[simp]
 theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) :=
@@ -337,10 +304,7 @@ theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app
 
 /- warning: Top.presheaf.pushforward.id_inv_app' -> TopCat.Presheaf.Pushforward.id_inv_app' is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)) (p : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (CategoryTheory.Iso.inv.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (p : IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) (CategoryTheory.Iso.inv.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'ₓ'. -/
 @[simp]
 theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
@@ -369,10 +333,7 @@ theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* 
 -/
 
 /- warning: Top.presheaf.pushforward.comp_hom_app -> TopCat.Presheaf.Pushforward.comp_hom_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_appₓ'. -/
 @[simp]
 theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
@@ -382,10 +343,7 @@ theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
 #align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_app
 
 /- warning: Top.presheaf.pushforward.comp_inv_app -> TopCat.Presheaf.Pushforward.comp_inv_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (CategoryTheory.Iso.inv.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (CategoryTheory.Iso.inv.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_appₓ'. -/
 @[simp]
 theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
@@ -446,10 +404,7 @@ def pullbackMap {X Y : TopCat.{v}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α :
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
 
 /- warning: Top.presheaf.pullback_obj_obj_of_image_open -> TopCat.Presheaf.pullbackObjObjOfImageOpen is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (H : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y) (Set.image.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (fun (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} X Y) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U))), CategoryTheory.Iso.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y) (Set.image.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (fun (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} X Y) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U)) H)))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (H : IsOpen.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (TopCat.topologicalSpace_forget.{u1} Y) (Set.image.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y f) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))), CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.image.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y f) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) H)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_obj_obj_of_image_open TopCat.Presheaf.pullbackObjObjOfImageOpenₓ'. -/
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
@@ -499,10 +454,7 @@ def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
 #align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.id
 
 /- warning: Top.presheaf.pullback.id_inv_app -> TopCat.Presheaf.Pullback.id_inv_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) (CategoryTheory.Iso.inv.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) ℱ (TopCat.Presheaf.Pullback.id.{u1, u2} C _inst_1 _inst_2 Y ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) C _inst_1 (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) _inst_2) (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.CostructuredArrow.mk.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) True) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) True (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) ((fun (a : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (a_1 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (e_1 : Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a a_1) (ᾰ : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (ᾰ_1 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (e_2 : Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) ᾰ ᾰ_1) => congr.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) -> Prop) a a_1 (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))) e_1) e_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (TopologicalSpace.Opens.op_map_id_obj.{u1} Y (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (rfl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (propext (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) (Opposite.op_inj_iff.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U))) (propext (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) True (eq_self_iff_true.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)))) trivial))))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) (CategoryTheory.Iso.inv.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) ℱ (TopCat.Presheaf.Pullback.id.{u1, u2} C _inst_1 _inst_2 Y ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) C _inst_1 (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) _inst_2) (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.CostructuredArrow.mk.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) True (congrFun.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (fun (a._@.Init.Prelude._hyg.170 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) => Prop) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (congrArg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) -> Prop) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))) (TopologicalSpace.Opens.op_map_id_obj.{u1} Y (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback.id_inv_app TopCat.Presheaf.Pullback.id_inv_appₓ'. -/
 theorem id_inv_app (U : Opens Y) :
     (id ℱ).inv.app (op U) =
@@ -537,10 +489,7 @@ def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
 #align Top.presheaf.pushforward TopCat.Presheaf.pushforward
 
 /- warning: Top.presheaf.pushforward_map_app' -> TopCat.Presheaf.pushforward_map_app' is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (α : Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))) ℱ 𝒢) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))}, Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) 𝒢) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ) (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) 𝒢) (CategoryTheory.Functor.map.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ 𝒢 α) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ 𝒢 α (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U))))
-but is expected to have type
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (α : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) ℱ 𝒢) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))}, Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) 𝒢)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ) (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) 𝒢) (Prefunctor.map.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ 𝒢 α) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ 𝒢 α (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'ₓ'. -/
 @[simp]
 theorem pushforward_map_app' {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (α : ℱ ⟶ 𝒢)
@@ -597,10 +546,7 @@ def toPushforwardOfIso {X Y : TopCat} (H : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 :
 #align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIso
 
 /- warning: Top.presheaf.to_pushforward_of_iso_app -> TopCat.Presheaf.toPushforwardOfIso_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} (H₂ : Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢) (U : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) U)) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) (TopCat.Presheaf.toPushforwardOfIso.{u1, u2, u3} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) U) (CategoryTheory.Functor.map.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.eqToHom.{u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Eq.mpr.{0} (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) True) (Eq.trans.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True ((fun (a : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (a_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_1 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a a_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, 1} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> Prop) a a_1 (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) e_1) e_2) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) e_1) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) e_1) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (e_1 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1 (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) e_1) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) (Eq.trans.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) carrier) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) ((fun [_inst_1 : TopologicalSpace.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)] (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => Eq.drec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => forall (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier), Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open') (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier_1 (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) is_open' carrier_1 e_2))) (fun (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) => rfl.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open')) carrier_1 e_2) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk_coe.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op_unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (propext (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True (eq_self_iff_true.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U)))) trivial))) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢 H₂ (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H₁ : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y} (H₂ : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢) (TopCat.Presheaf.toPushforwardOfIso.{u2, u3, u1} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 𝒢) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) U (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) True (congrArg.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) Prop (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U) (congrArg.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((fun {α : Type.{u1}} [inst._@.Mathlib.Topology.Sets.Opens._hyg.47 : TopologicalSpace.{u1} α] (carrier : Set.{u1} α) (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => Eq.rec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => forall (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier), Eq.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open') (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier_1 (Eq.ndrec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier : Set.{u1} α) => IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) is_open' carrier_1 e_carrier))) (fun (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) => Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open')) carrier_1 e_carrier) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U))))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢 H₂ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_appₓ'. -/
 @[simp]
 theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 : Y.Presheaf C}
@@ -632,10 +578,7 @@ def pushforwardToOfIso {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {
 #align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIso
 
 /- warning: Top.presheaf.pushforward_to_of_iso_app -> TopCat.Presheaf.pushforwardToOfIso_app is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} (H₂ : Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢)) (U : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 U)) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢 (TopCat.Presheaf.pushforwardToOfIso.{u1, u2, u3} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 U) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) H₂ (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (CategoryTheory.Functor.map.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (CategoryTheory.eqToHom.{u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.mpr.{0} (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) True) (Eq.trans.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True ((fun (a : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (a_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_1 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a a_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, 1} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> Prop) a a_1 (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) e_1) e_2) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) e_1) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) e_1) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (e_1 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1 (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) e_1) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) (Eq.trans.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) carrier) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) ((fun [_inst_1 : TopologicalSpace.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)] (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => Eq.drec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => forall (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier), Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open') (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier_1 (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) is_open' carrier_1 e_2))) (fun (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) => rfl.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open')) carrier_1 e_2) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk_coe.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op_unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (propext (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True (eq_self_iff_true.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U)))) trivial))))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H₁ : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (H₂ : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢 (TopCat.Presheaf.pushforwardToOfIso.{u2, u3, u1} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢) H₂ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) U (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) U) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) U) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) U) True (congrFun.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (fun (a._@.Init.Prelude._hyg.170 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) => Prop) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (congrArg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) -> Prop) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))) (congrArg.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((fun {α : Type.{u1}} [inst._@.Mathlib.Topology.Sets.Opens._hyg.47 : TopologicalSpace.{u1} α] (carrier : Set.{u1} α) (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => Eq.rec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => forall (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier), Eq.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open') (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier_1 (Eq.ndrec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier : Set.{u1} α) => IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) is_open' carrier_1 e_carrier))) (fun (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) => Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open')) carrier_1 e_carrier) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) U) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_to_of_iso_app TopCat.Presheaf.pushforwardToOfIso_appₓ'. -/
 @[simp]
 theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {𝒢 : X.Presheaf C}

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Adjunction.Opposites
 /-!
 # Presheaves on a topological space
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define `presheaf C X` simply as `(opens X)ᵒᵖ ⥤ C`,
 and inherit the category structure with natural transformations as morphisms.
 

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

@@ -44,11 +44,13 @@ variable (C : Type u) [Category.{v} C]
 
 namespace TopCat
 
+#print TopCat.Presheaf /-
 /-- The category of `C`-valued presheaves on a (bundled) topological space `X`. -/
 @[nolint has_nonempty_instance]
 def Presheaf (X : TopCat.{w}) : Type max u v w :=
   (Opens X)ᵒᵖ ⥤ C deriving Category
 #align Top.presheaf TopCat.Presheaf
+-/
 
 variable {C}
 
@@ -96,6 +98,12 @@ example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓
   run_tac
     restrict_tac'
 
+/- warning: Top.presheaf.restrict -> TopCat.Presheaf.restrict is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (forall {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))))) U V) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))))
+but is expected to have type
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) V))) -> (forall {U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) U V) -> (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict TopCat.Presheaf.restrictₓ'. -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
 and the notation `x |_ₗ U ⟪i⟫` (`l` stands for `le`) for `i : U ≤ V`.
@@ -113,6 +121,12 @@ scoped[AlgebraicGeometry]
   notation:80 x " |_ₗ " U " ⟪" e "⟫ " =>
     @TopCat.Presheaf.restrict _ _ _ _ _ _ x U (@homOfLE (Opens _) _ U _ e)
 
+/- warning: Top.presheaf.restrict_open -> TopCat.Presheaf.restrictOpen is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)}, (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (forall (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)), (autoParamₓ.{0} (LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 39 (OfNat.mk.{0} Nat 39 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 112 (OfNat.mk.{0} Nat 112 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 104 (OfNat.mk.{0} Nat 104 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 84 (OfNat.mk.{0} Nat 84 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 112 (OfNat.mk.{0} Nat 112 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous)))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))))
+but is expected to have type
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) V))) -> (forall (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)), (autoParam.{0} (LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) U V) _auto._@.Mathlib.Topology.Sheaves.Presheaf._hyg.1775) -> (Prefunctor.obj.{succ u3, succ u4, u2, succ u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) Type.{u4} (CategoryTheory.CategoryStruct.toQuiver.{u4, succ u4} Type.{u4} (CategoryTheory.Category.toCategoryStruct.{u4, succ u4} Type.{u4} CategoryTheory.types.{u4})) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u2, succ u4} C _inst_2 Type.{u4} CategoryTheory.types.{u4} (CategoryTheory.forget.{u2, u4, u3} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u1, succ u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_2 F) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_open TopCat.Presheaf.restrictOpenₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ U`, where the proof `U ≤ V` is inferred by
@@ -129,6 +143,12 @@ abbrev restrictOpen {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
 -- mathport name: «expr |_ »
 scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
+/- warning: Top.presheaf.restrict_restrict -> TopCat.Presheaf.restrict_restrict is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {W : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} (e₁ : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (e₂ : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) V W) (x : coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) W))), Eq.{succ u4} (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F V (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F W x V e₂) U e₁) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F W x U (le_trans.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)))) U V W e₁ e₂))
+but is expected to have type
+  forall {X : TopCat.{u4}} {C : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u2, u3} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_2] {F : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} {U : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {V : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {W : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} (e₁ : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) U V) (e₂ : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) V W) (x : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W))), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F V (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F W x V (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W a)) (e₂ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a) a_1))))))) U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (e₁ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1))))))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F W x U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a W)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) W a)) (e₂ a (Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (e₁ a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrictₓ'. -/
 @[simp]
 theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
@@ -138,6 +158,12 @@ theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCatego
   rfl
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
 
+/- warning: Top.presheaf.map_restrict -> TopCat.Presheaf.map_restrict is a dubious translation:
+lean 3 declaration is
+  forall {X : TopCat.{u1}} {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u3, u2} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u4, u3, u2} C _inst_2] {F : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} {G : TopCat.Presheaf.{u1, u3, u2} C _inst_2 X} (e : Quiver.Hom.{succ (max u1 u3), max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max u2 u3 u1} (TopCat.Presheaf.{u1, u3, u2} C _inst_2 X) (TopCat.Presheaf.category.{u3, u1, u2} C _inst_2 X))) F G) {U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} {V : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)} (h : LE.le.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U V) (x : coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))), Eq.{succ u4} (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (coeFn.{succ u3, succ u4} (Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (fun (f : Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) => (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u3, u4} C _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U))) (CategoryTheory.NatTrans.app.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F G e (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 F V x U h)) (TopCat.Presheaf.restrictOpen.{u1, u2, u3, u4} X C _inst_2 _inst_3 G V (coeFn.{succ u3, succ u4} (Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) (fun (f : Quiver.Hom.{succ u3, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} C (CategoryTheory.Category.toCategoryStruct.{u3, u2} C _inst_2)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) => (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) -> (coeSort.{succ u2, succ (succ u4)} C Type.{u4} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u4, u3} C _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u3, u4} C _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) (CategoryTheory.Functor.obj.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 G (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V))) (CategoryTheory.NatTrans.app.{u1, u3, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_2 F G e (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) V)) x) U h)
+but is expected to have type
+  forall {X : TopCat.{u4}} {C : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u2, u3} C] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_2] {F : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} {G : TopCat.Presheaf.{u4, u2, u3} C _inst_2 X} (e : Quiver.Hom.{max (succ u2) (succ u4), max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max (max u3 u2) u4} (TopCat.Presheaf.{u4, u2, u3} C _inst_2 X) (TopCat.instCategoryPresheaf.{u4, u2, u3} C _inst_2 X))) F G) {U : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} {V : TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)} (h : LE.le.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.toLE.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)))))) U V) (x : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V))), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U))) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (CategoryTheory.NatTrans.app.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F G e (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 F V x U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (h a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))) (TopCat.Presheaf.restrictOpen.{u4, u3, u2, u1} X C _inst_2 _inst_3 G V (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_2 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_2 _inst_3)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Prefunctor.obj.{succ u4, succ u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.CategoryStruct.toQuiver.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.toCategoryStruct.{u4, u4} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 G) (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (CategoryTheory.NatTrans.app.{u4, u2, u4, u3} (Opposite.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) (CategoryTheory.Category.opposite.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (Preorder.smallCategory.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (PartialOrder.toPreorder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteSemilatticeInf.toPartialOrder.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CompleteLattice.toCompleteSemilatticeInf.{u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))))))) C _inst_2 F G e (Opposite.op.{succ u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) x) U (fun {{a : CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X}} (a_1 : Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) => Eq.mpr.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V) (id.{0} (Eq.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a V)) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) V a)) (h a (of_eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Eq.trans.{1} Prop (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) True (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) (eq_true (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Eq.mp.{0} (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (Set.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) (Set.instMembershipSet.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X)) a (SetLike.coe.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U)) (Membership.mem.{u4, u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (SetLike.instMembership.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X))) a U) (Mathlib.Data.SetLike.Basic._auxLemma.2.{u4, u4} (TopologicalSpace.Opens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopologicalSpace.Opens.instSetLikeOpens.{u4} (CategoryTheory.Bundled.α.{u4, u4} TopologicalSpace.{u4} X) (TopCat.topologicalSpace_coe.{u4} X)) U a) a_1)))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.map_restrict TopCat.Presheaf.map_restrictₓ'. -/
 @[simp]
 theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
@@ -147,27 +173,47 @@ theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
   rw [← comp_apply, nat_trans.naturality, comp_apply]
 #align Top.presheaf.map_restrict TopCat.Presheaf.map_restrict
 
+#print TopCat.Presheaf.pushforwardObj /-
 /-- Pushforward a presheaf on `X` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `Y`. -/
 def pushforwardObj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) : Y.Presheaf C :=
   (Opens.map f).op ⋙ ℱ
 #align Top.presheaf.pushforward_obj TopCat.Presheaf.pushforwardObj
+-/
 
 -- mathport name: «expr _* »
 infixl:80 " _* " => pushforwardObj
 
+/- warning: Top.presheaf.pushforward_obj_obj -> TopCat.Presheaf.pushforwardObj_obj is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u3} C (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u3} C (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_objₓ'. -/
 @[simp]
 theorem pushforwardObj_obj {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U : (Opens Y)ᵒᵖ) :
     (f _* ℱ).obj U = ℱ.obj ((Opens.map f).op.obj U) :=
   rfl
 #align Top.presheaf.pushforward_obj_obj TopCat.Presheaf.pushforwardObj_obj
 
+/- warning: Top.presheaf.pushforward_obj_map -> TopCat.Presheaf.pushforwardObj_map is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))} {V : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))} (i : Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (Quiver.opposite.{u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))))) U V), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) V)) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U V i) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) V) (CategoryTheory.Functor.map.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U V i))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))} {V : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))} (i : Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Quiver.opposite.{u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) U V), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) V)) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U V i) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) V) (Prefunctor.map.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U V i))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_mapₓ'. -/
 @[simp]
 theorem pushforwardObj_map {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) {U V : (Opens Y)ᵒᵖ}
     (i : U ⟶ V) : (f _* ℱ).map i = ℱ.map ((Opens.map f).op.map i) :=
   rfl
 #align Top.presheaf.pushforward_obj_map TopCat.Presheaf.pushforwardObj_map
 
+/- warning: Top.presheaf.pushforward_eq -> TopCat.Presheaf.pushforwardEq is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y}, (Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) -> (forall (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y}, (Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) -> (forall (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq TopCat.Presheaf.pushforwardEqₓ'. -/
 /--
 An equality of continuous maps induces a natural isomorphism between the pushforwards of a presheaf
 along those maps.
@@ -177,10 +223,18 @@ def pushforwardEq {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Preshe
   isoWhiskerRight (NatIso.op (Opens.mapIso f g h).symm) ℱ
 #align Top.presheaf.pushforward_eq TopCat.Presheaf.pushforwardEq
 
+#print TopCat.Presheaf.pushforward_eq' /-
 theorem pushforward_eq' {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) :
     f _* ℱ = g _* ℱ := by rw [h]
 #align Top.presheaf.pushforward_eq' TopCat.Presheaf.pushforward_eq'
+-/
 
+/- warning: Top.presheaf.pushforward_eq_hom_app -> TopCat.Presheaf.pushforwardEq_hom_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (id.{succ u1} (Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Quiver.Hom.op.{u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.eqToHom.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.mpr.{0} (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y _a) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) (rfl.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))) g h)) (rfl.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))))))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (id.{succ u1} (Quiver.Hom.{succ u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Quiver.Hom.op.{u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.eqToHom.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.mpr.{0} (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (id.{0} (Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y _a)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) (Eq.refl.{1} Prop (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))) g h)) (Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_appₓ'. -/
 @[simp]
 theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq h ℱ).Hom.app U =
@@ -188,11 +242,23 @@ theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (
   by simp [pushforward_eq]
 #align Top.presheaf.pushforward_eq_hom_app TopCat.Presheaf.pushforwardEq_hom_app
 
+/- warning: Top.presheaf.pushforward_eq'_hom_app -> TopCat.Presheaf.pushforward_eq'_hom_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.eqToHom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforward_eq'.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y _a)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) (rfl.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f)) U) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U))) g h)) (rfl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y g)) U)))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (CategoryTheory.eqToHom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ) (TopCat.Presheaf.pushforward_eq'.{u1, u2, u3} C _inst_1 X Y f g h ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (id.{0} (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) (Eq.ndrec.{0, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f (fun (_a : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) => Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y _a))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) (Eq.refl.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f))) U) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U))) g h)) (Eq.refl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y g))) U)))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_appₓ'. -/
 theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (ℱ : X.Presheaf C)
     (U) : NatTrans.app (eqToHom (pushforward_eq' h ℱ)) U = ℱ.map (eqToHom (by rw [h])) := by
   simpa [eq_to_hom_map]
 #align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_app
 
+/- warning: Top.presheaf.pushforward_eq_rfl -> TopCat.Presheaf.pushforwardEq_rfl is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f f (rfl.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f f (rfl.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rflₓ'. -/
 @[simp]
 theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq (rfl : f = f) ℱ).Hom.app (op U) = 𝟙 _ :=
@@ -201,6 +267,12 @@ theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C)
   simp
 #align Top.presheaf.pushforward_eq_rfl TopCat.Presheaf.pushforwardEq_rfl
 
+/- warning: Top.presheaf.pushforward_eq_eq -> TopCat.Presheaf.pushforwardEq_eq is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y} (h₁ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (h₂ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), Eq.{succ (max u1 u2)} (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₁ ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₂ ℱ)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y} (h₁ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (h₂ : Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) f g) (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), Eq.{max (succ u2) (succ u1)} (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y g ℱ)) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₁ ℱ) (TopCat.Presheaf.pushforwardEq.{u1, u2, u3} C _inst_1 X Y f g h₂ ℱ)
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_eq_eq TopCat.Presheaf.pushforwardEq_eqₓ'. -/
 theorem pushforwardEq_eq {X Y : TopCat.{w}} {f g : X ⟶ Y} (h₁ h₂ : f = g) (ℱ : X.Presheaf C) :
     ℱ.pushforwardEq h₁ = ℱ.pushforwardEq h₂ :=
   rfl
@@ -210,18 +282,32 @@ namespace Pushforward
 
 variable {X : TopCat.{w}} (ℱ : X.Presheaf C)
 
+/- warning: Top.presheaf.pushforward.id -> TopCat.Presheaf.Pushforward.id is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id TopCat.Presheaf.Pushforward.idₓ'. -/
 /-- The natural isomorphism between the pushforward of a presheaf along the identity continuous map
 and the original presheaf. -/
 def id : 𝟙 X _* ℱ ≅ ℱ :=
   isoWhiskerRight (NatIso.op (Opens.mapId X).symm) ℱ ≪≫ Functor.leftUnitor _
 #align Top.presheaf.pushforward.id TopCat.Presheaf.Pushforward.id
 
+#print TopCat.Presheaf.Pushforward.id_eq /-
 theorem id_eq : 𝟙 X _* ℱ = ℱ := by
   unfold pushforward_obj
   rw [opens.map_id_eq]
   erw [functor.id_comp]
 #align Top.presheaf.pushforward.id_eq TopCat.Presheaf.Pushforward.id_eq
+-/
 
+/- warning: Top.presheaf.pushforward.id_hom_app' -> TopCat.Presheaf.Pushforward.id_hom_app' is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)) (p : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (p : IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'ₓ'. -/
 @[simp]
 theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
   by
@@ -231,6 +317,12 @@ theorem id_hom_app' (U) (p) : (id ℱ).Hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (
 
 attribute [local tidy] tactic.op_induction'
 
+/- warning: Top.presheaf.pushforward.id_hom_app -> TopCat.Presheaf.Pushforward.id_hom_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) U) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) U) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) U) U (TopologicalSpace.Opens.op_map_id_obj.{u1} X U)))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) U) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)))) U) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)))) U) U (TopologicalSpace.Opens.op_map_id_obj.{u1} X U)))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_appₓ'. -/
 @[simp]
 theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) :=
   by
@@ -241,6 +333,12 @@ theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_
   congr
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app
 
+/- warning: Top.presheaf.pushforward.id_inv_app' -> TopCat.Presheaf.Pushforward.id_inv_app' is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X)) (p : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) (CategoryTheory.Iso.inv.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.Functor.map.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X) U p))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (U : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (p : IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) (CategoryTheory.Iso.inv.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X) ℱ) ℱ (TopCat.Presheaf.Pushforward.id.{u1, u2, u3} C _inst_1 X ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p)) (CategoryTheory.CategoryStruct.id.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) U p))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'ₓ'. -/
 @[simp]
 theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) :=
   by
@@ -248,6 +346,12 @@ theorem id_inv_app' (U) (p) : (id ℱ).inv.app (op ⟨U, p⟩) = ℱ.map (𝟙 (
   simp
 #align Top.presheaf.pushforward.id_inv_app' TopCat.Presheaf.Pushforward.id_inv_app'
 
+/- warning: Top.presheaf.pushforward.comp -> TopCat.Presheaf.Pushforward.comp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z), CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z), CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp TopCat.Presheaf.Pushforward.compₓ'. -/
 /-- The natural isomorphism between
 the pushforward of a presheaf along the composition of two continuous maps and
 the corresponding pushforward of a pushforward. -/
@@ -255,10 +359,18 @@ def comp {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* ℱ ≅ g
   isoWhiskerRight (NatIso.op (Opens.mapComp f g).symm) ℱ
 #align Top.presheaf.pushforward.comp TopCat.Presheaf.Pushforward.comp
 
+#print TopCat.Presheaf.Pushforward.comp_eq /-
 theorem comp_eq {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g) _* ℱ = g _* (f _* ℱ) :=
   rfl
 #align Top.presheaf.pushforward.comp_eq TopCat.Presheaf.Pushforward.comp_eq
+-/
 
+/- warning: Top.presheaf.pushforward.comp_hom_app -> TopCat.Presheaf.Pushforward.comp_hom_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (CategoryTheory.Iso.hom.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (CategoryTheory.Iso.hom.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_appₓ'. -/
 @[simp]
 theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).Hom.app U = 𝟙 _ := by
@@ -266,6 +378,12 @@ theorem comp_hom_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
   tidy
 #align Top.presheaf.pushforward.comp_hom_app TopCat.Presheaf.Pushforward.comp_hom_app
 
+/- warning: Top.presheaf.pushforward.comp_inv_app -> TopCat.Presheaf.Pushforward.comp_inv_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (CategoryTheory.Iso.inv.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (CategoryTheory.Functor.category.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Z) (TopCat.topologicalSpace.{u1} Z)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) U))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopCat.{u1}} {Z : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (CategoryTheory.Iso.inv.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Z) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X Y Z f g) ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ)) (TopCat.Presheaf.Pushforward.comp.{u1, u2, u3} C _inst_1 X ℱ Y Z f g)) U) (CategoryTheory.CategoryStruct.id.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Z) (TopCat.topologicalSpace_coe.{u1} Z))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y Z g (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ))) U))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward.comp_inv_app TopCat.Presheaf.Pushforward.comp_inv_appₓ'. -/
 @[simp]
 theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (comp ℱ f g).inv.app U = 𝟙 _ := by
@@ -275,6 +393,12 @@ theorem comp_inv_app {Y Z : TopCat.{w}} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
 
 end Pushforward
 
+/- warning: Top.presheaf.pushforward_map -> TopCat.Presheaf.pushforwardMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))) ℱ 𝒢) -> (Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f 𝒢))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) ℱ 𝒢) -> (Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f ℱ) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y f 𝒢))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_map TopCat.Presheaf.pushforwardMapₓ'. -/
 /-- A morphism of presheaves gives rise to a morphisms of the pushforwards of those presheaves.
 -/
 @[simps]
@@ -294,6 +418,7 @@ variable [HasColimits C]
 
 noncomputable section
 
+#print TopCat.Presheaf.pullbackObj /-
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf on `X`.
 
 This is defined in terms of left Kan extensions, which is just a fancy way of saying
@@ -303,13 +428,26 @@ This is defined in terms of left Kan extensions, which is just a fancy way of sa
 def pullbackObj {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) : X.Presheaf C :=
   (lan (Opens.map f).op).obj ℱ
 #align Top.presheaf.pullback_obj TopCat.Presheaf.pullbackObj
+-/
 
+/- warning: Top.presheaf.pullback_map -> TopCat.Presheaf.pullbackMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y))) ℱ 𝒢) -> (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1))) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f 𝒢))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y))) ℱ 𝒢) -> (Quiver.Hom.{succ u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X))) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f 𝒢))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMapₓ'. -/
 /-- Pulling back along continuous maps is functorial. -/
 def pullbackMap {X Y : TopCat.{v}} (f : X ⟶ Y) {ℱ 𝒢 : Y.Presheaf C} (α : ℱ ⟶ 𝒢) :
     pullbackObj f ℱ ⟶ pullbackObj f 𝒢 :=
   (lan (Opens.map f).op).map α
 #align Top.presheaf.pullback_map TopCat.Presheaf.pullbackMap
 
+/- warning: Top.presheaf.pullback_obj_obj_of_image_open -> TopCat.Presheaf.pullbackObjObjOfImageOpen is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (H : IsOpen.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y) (Set.image.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (fun (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} X Y) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U))), CategoryTheory.Iso.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y) (Set.image.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (fun (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) => (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) -> (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} X Y) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (Set.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X)) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) X) (TopCat.topologicalSpace.{u1} X))))) U)) H)))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (H : IsOpen.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (TopCat.topologicalSpace_forget.{u1} Y) (Set.image.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y f) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))), CategoryTheory.Iso.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 X Y f ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.image.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y f) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) H)))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_obj_obj_of_image_open TopCat.Presheaf.pullbackObjObjOfImageOpenₓ'. -/
 /-- If `f '' U` is open, then `f⁻¹ℱ U ≅ ℱ (f '' U)`.  -/
 @[simps]
 def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf C) (U : Opens X)
@@ -337,6 +475,12 @@ namespace Pullback
 
 variable {X Y : TopCat.{v}} (ℱ : Y.Presheaf C)
 
+/- warning: Top.presheaf.pullback.id -> TopCat.Presheaf.Pullback.id is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y), CategoryTheory.Iso.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) ℱ
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y), CategoryTheory.Iso.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) ℱ
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.idₓ'. -/
 /-- The pullback along the identity is isomorphic to the original presheaf. -/
 def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
   NatIso.ofComponents
@@ -351,6 +495,12 @@ def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
     dsimp; simp only [← ℱ.map_comp]; congr
 #align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.id
 
+/- warning: Top.presheaf.pullback.id_inv_app -> TopCat.Presheaf.Pullback.id_inv_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 ℱ (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) (CategoryTheory.Iso.inv.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (CategoryTheory.Functor.category.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y) ℱ) ℱ (TopCat.Presheaf.Pullback.id.{u1, u2} C _inst_1 _inst_2 Y ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) C _inst_1 (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (CategoryTheory.CostructuredArrow.category.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) _inst_2) (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (CategoryTheory.CostructuredArrow.mk.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Eq.mpr.{0} (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) True) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) True (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) ((fun (a : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (a_1 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (e_1 : Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a a_1) (ᾰ : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (ᾰ_1 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (e_2 : Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) ᾰ ᾰ_1) => congr.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) -> Prop) a a_1 (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))) e_1) e_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (TopologicalSpace.Opens.op_map_id_obj.{u1} Y (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U) (rfl.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) U))) (propext (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)) (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) (Opposite.op_inj_iff.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U))) (propext (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U U) True (eq_self_iff_true.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U)))) trivial))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {Y : TopCat.{u1}} (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (U : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) (CategoryTheory.Iso.inv.{u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_1 _inst_2 Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y) ℱ) ℱ (TopCat.Presheaf.Pullback.id.{u1, u2} C _inst_1 _inst_2 Y ℱ)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) C _inst_1 (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, u1, u2} C _inst_1 (CategoryTheory.CostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (CategoryTheory.instCategoryCostructuredArrow.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) _inst_2) (CategoryTheory.Lan.diagram.{u1, u1, u1, u1, u1, u2} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) C (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) ℱ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (CategoryTheory.CostructuredArrow.mk.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) True (congrFun.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (fun (a._@.Init.Prelude._hyg.170 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) => Prop) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (congrArg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) -> Prop) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y Y (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) Y)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))) (TopologicalSpace.Opens.op_map_id_obj.{u1} Y (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U)))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback.id_inv_app TopCat.Presheaf.Pullback.id_inv_appₓ'. -/
 theorem id_inv_app (U : Opens Y) :
     (id ℱ).inv.app (op U) =
       colimit.ι (Lan.diagram (Opens.map (𝟙 Y)).op ℱ (op U))
@@ -369,6 +519,12 @@ end Pullback
 
 variable (C)
 
+/- warning: Top.presheaf.pushforward -> TopCat.Presheaf.pushforward is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y))
+but is expected to have type
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward TopCat.Presheaf.pushforwardₓ'. -/
 /-- The pushforward functor.
 -/
 def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
@@ -377,12 +533,24 @@ def pushforward {X Y : TopCat.{w}} (f : X ⟶ Y) : X.Presheaf C ⥤ Y.Presheaf C
   map := @pushforwardMap _ _ X Y f
 #align Top.presheaf.pushforward TopCat.Presheaf.pushforward
 
+/- warning: Top.presheaf.pushforward_map_app' -> TopCat.Presheaf.pushforward_map_app' is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (α : Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))) ℱ 𝒢) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y))}, Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ) U) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) 𝒢) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)))))) C _inst_1 (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ) (CategoryTheory.Functor.obj.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) 𝒢) (CategoryTheory.Functor.map.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f) ℱ 𝒢 α) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)))))) C _inst_1 ℱ 𝒢 α (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} Y) (TopCat.topologicalSpace.{u1} Y))))) (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopologicalSpace.Opens.setLike.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))))) (TopologicalSpace.Opens.map.{u1} X Y f) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u1, u1, u1} TopCat.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}) Y) (TopCat.topologicalSpace.{u1} Y)) U))))
+but is expected to have type
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (α : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) ℱ 𝒢) {U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))}, Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) 𝒢)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ) (Prefunctor.obj.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) 𝒢) (Prefunctor.map.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X Y f)) ℱ 𝒢 α) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ 𝒢 α (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y f)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) U))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'ₓ'. -/
 @[simp]
 theorem pushforward_map_app' {X Y : TopCat.{w}} (f : X ⟶ Y) {ℱ 𝒢 : X.Presheaf C} (α : ℱ ⟶ 𝒢)
     {U : (Opens Y)ᵒᵖ} : ((pushforward C f).map α).app U = α.app (op <| (Opens.map f).obj U.unop) :=
   rfl
 #align Top.presheaf.pushforward_map_app' TopCat.Presheaf.pushforward_map_app'
 
+/- warning: Top.presheaf.id_pushforward -> TopCat.Presheaf.id_pushforward is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}}, Eq.{succ (max (max u1 u2) u3 u2 u1)} (CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X)) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1}) X)) (CategoryTheory.Functor.id.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X))
+but is expected to have type
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}}, Eq.{max (max (succ u3) (succ u2)) (succ u1)} (CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X)) (TopCat.Presheaf.pushforward.{u1, u2, u3} C _inst_1 X X (CategoryTheory.CategoryStruct.id.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) X)) (CategoryTheory.Functor.id.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforwardₓ'. -/
 theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presheaf C) :=
   by
   apply CategoryTheory.Functor.ext
@@ -397,6 +565,12 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
 
 section Iso
 
+/- warning: Top.presheaf.presheaf_equiv_of_iso -> TopCat.Presheaf.presheafEquivOfIso is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}}, (CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) -> (CategoryTheory.Equivalence.{max u3 u1, max u3 u1, max u2 u1 u3, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X) (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}}, (CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) -> (CategoryTheory.Equivalence.{max u1 u3, max u1 u3, max (max u2 u1) u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.presheaf_equiv_of_iso TopCat.Presheaf.presheafEquivOfIsoₓ'. -/
 /-- A homeomorphism of spaces gives an equivalence of categories of presheaves. -/
 @[simps]
 def presheafEquivOfIso {X Y : TopCat} (H : X ≅ Y) : X.Presheaf C ≌ Y.Presheaf C :=
@@ -405,6 +579,12 @@ def presheafEquivOfIso {X Y : TopCat} (H : X ≅ Y) : X.Presheaf C ≌ Y.Preshea
 
 variable {C}
 
+/- warning: Top.presheaf.to_pushforward_of_iso -> TopCat.Presheaf.toPushforwardOfIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y}, (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H) ℱ) 𝒢) -> (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H) 𝒢))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H) ℱ) 𝒢) -> (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H) 𝒢))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIsoₓ'. -/
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -413,6 +593,12 @@ def toPushforwardOfIso {X Y : TopCat} (H : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 :
   (presheafEquivOfIso _ H).toAdjunction.homEquiv ℱ 𝒢 α
 #align Top.presheaf.to_pushforward_of_iso TopCat.Presheaf.toPushforwardOfIso
 
+/- warning: Top.presheaf.to_pushforward_of_iso_app -> TopCat.Presheaf.toPushforwardOfIso_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} (H₂ : Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢) (U : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) U)) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) (TopCat.Presheaf.toPushforwardOfIso.{u1, u2, u3} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) U) (CategoryTheory.Functor.map.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 ℱ U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.eqToHom.{u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Eq.mpr.{0} (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) True) (Eq.trans.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True ((fun (a : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (a_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_1 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a a_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, 1} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> Prop) a a_1 (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) e_1) e_2) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) e_1) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) e_1) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (e_1 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1 (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) e_1) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) (Eq.trans.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) carrier) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) ((fun [_inst_1 : TopologicalSpace.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)] (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => Eq.drec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => forall (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier), Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open') (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier_1 (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) is_open' carrier_1 e_2))) (fun (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) => rfl.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open')) carrier_1 e_2) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk_coe.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op_unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (propext (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True (eq_self_iff_true.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U)))) trivial))) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢 H₂ (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H₁ : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y} (H₂ : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢) (TopCat.Presheaf.toPushforwardOfIso.{u2, u3, u1} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 𝒢) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 ℱ) U (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) U (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) True (congrArg.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) Prop (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U) (congrArg.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((fun {α : Type.{u1}} [inst._@.Mathlib.Topology.Sets.Opens._hyg.47 : TopologicalSpace.{u1} α] (carrier : Set.{u1} α) (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => Eq.rec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => forall (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier), Eq.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open') (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier_1 (Eq.ndrec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier : Set.{u1} α) => IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) is_open' carrier_1 e_carrier))) (fun (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) => Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open')) carrier_1 e_carrier) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U))))) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢 H₂ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_appₓ'. -/
 @[simp]
 theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf C} {𝒢 : Y.Presheaf C}
     (H₂ : H₁.Hom _* ℱ ⟶ 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -428,6 +614,12 @@ theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf
   congr
 #align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_app
 
+/- warning: Top.presheaf.pushforward_to_of_iso -> TopCat.Presheaf.pushforwardToOfIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X}, (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢)) -> (Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 X))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H₁) 𝒢)) -> (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u3, u1, u2} C _inst_1 X))) (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} instTopCatLargeCategory.{u3} X Y H₁) ℱ) 𝒢)
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIsoₓ'. -/
 /-- If `H : X ≅ Y` is a homeomorphism,
 then given an `H _* ℱ ⟶ 𝒢`, we may obtain an `ℱ ⟶ H ⁻¹ _* 𝒢`.
 -/
@@ -436,6 +628,12 @@ def pushforwardToOfIso {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {
   ((presheafEquivOfIso _ H₁.symm).toAdjunction.homEquiv ℱ 𝒢).symm H₂
 #align Top.presheaf.pushforward_to_of_iso TopCat.Presheaf.pushforwardToOfIso
 
+/- warning: Top.presheaf.pushforward_to_of_iso_app -> TopCat.Presheaf.pushforwardToOfIso_app is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : TopCat.{u3}} {Y : TopCat.{u3}} (H₁ : CategoryTheory.Iso.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y) {ℱ : TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u3, u1, u2} C _inst_1 X} (H₂ : Quiver.Hom.{succ (max u3 u1), max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u1 u3} (TopCat.Presheaf.{u3, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u3, u2} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢)) (U : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 U)) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) 𝒢 (TopCat.Presheaf.pushforwardToOfIso.{u1, u2, u3} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) ℱ) U) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 U) (CategoryTheory.NatTrans.app.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u3, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) 𝒢) H₂ (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (CategoryTheory.Functor.map.{u3, u1, u3, u2} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) C _inst_1 𝒢 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (CategoryTheory.eqToHom.{u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.mpr.{0} (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) True) (Eq.trans.{1} Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True ((fun (a : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (a_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_1 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a a_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, 1} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) Prop (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a) (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) a_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> Prop) a a_1 (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) e_1) e_2) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) e_1) (TopologicalSpace.Opens.map.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Eq.trans.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) U) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (self : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (self_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) self self_1) (ᾰ : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (ᾰ_1 : Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (e_2 : Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1) => congr.{succ u3, succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) self_1) ᾰ ᾰ_1 (congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) ((Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) -> (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))) self self_1 (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) e_1) e_2) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)))) ((fun (F : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (F_1 : CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (e_1 : Eq.{succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) F F_1) => congr_arg.{succ u3, succ u3} (CategoryTheory.Functor.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) (CategoryTheory.Functor.{u3, u3, u3, u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)))))) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))) (CategoryTheory.Category.opposite.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) F F_1 (CategoryTheory.Functor.op.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)))))) e_1) (TopologicalSpace.Opens.map.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (TopologicalSpace.Opens.map.equations._eqn_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) U))) (CategoryTheory.Functor.op_obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (e_1 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) ᾰ ᾰ_1 (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) e_1) (CategoryTheory.Functor.obj.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (CategoryTheory.Functor.mk.{u3, u3, u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) => TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (fun (U : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (V : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (i : Quiver.Hom.{succ u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (CategoryTheory.Category.toCategoryStruct.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Preorder.smallCategory.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))))) U V) => ULift.up.{u3, 0} (PLift.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V)))) (PLift.up.{0} (LE.le.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Preorder.toHasLe.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (PartialOrder.toPreorder.{u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (SetLike.partialOrder.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) U)) (TopologicalSpace.Opens.map._proof_2.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) V)) (TopologicalSpace.Opens.map._proof_3.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) V))) (TopologicalSpace.Opens.map._proof_4.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) U V i))) (TopologicalSpace.Opens.map._proof_5.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (TopologicalSpace.Opens.map._proof_6.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) (Eq.trans.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) carrier) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U) ((fun [_inst_1 : TopologicalSpace.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)] (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => Eq.drec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier carrier_1) => forall (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier), Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open') (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier_1 (Eq.ndrec.{0, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) carrier (fun (carrier : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) => IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) is_open' carrier_1 e_2))) (fun (is_open' : IsOpen.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier) => rfl.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) _inst_1 carrier is_open')) carrier_1 e_2) (TopCat.topologicalSpace.{u3} X) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) e_1) e_2) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (rfl.{succ u3} ((fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Eq.trans.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) ((fun [_inst_1 : HasLiftT.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y))] (ᾰ : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (ᾰ_1 : TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (e_2 : Eq.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) ᾰ ᾰ_1) => congr_arg.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) ᾰ ᾰ_1 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) _inst_1) e_2) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (Opposite.unop_op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (TopologicalSpace.Opens.coe_mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_preimage.{u3, u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) ((fun (f : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (f_1 : (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_1 : Eq.{succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) f f_1) (s : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (s_1 : Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (e_2 : Eq.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) s s_1) => congr.{succ u3, succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X)) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) f_1) s s_1 (congr_arg.{succ u3, succ u3} ((coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) -> (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X))) f f_1 (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) e_1) e_2) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y)) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (funext.{succ u3, succ u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} Y X) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) (fun (f : Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) X Y) => (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) -> (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) Y)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3} X Y) (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) x)) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => x) (fun (x : coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) => CategoryTheory.Iso.hom_inv_id_apply.{u3, u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁ TopCat.concreteCategory.{u3} x)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) (rfl.{succ u3} (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Set.preimage_id'.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)))) (TopologicalSpace.Opens.map._proof_1.{u3} X Y (CategoryTheory.Iso.hom.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y)) (TopologicalSpace.Opens.mk.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (TopCat.topologicalSpace.{u3} Y) (Set.preimage.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (coeFn.{succ u3, succ u3} (Quiver.Hom.{succ u3, succ u3} TopCat.{u3} (CategoryTheory.CategoryStruct.toQuiver.{u3, succ u3} TopCat.{u3} (CategoryTheory.Category.toCategoryStruct.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3})) Y X) (fun (_x : ContinuousMap.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) => (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) -> (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (ContinuousMap.hasCoeToFun.{u3, u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) Y) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} Y) (CategoryTheory.Bundled.str.{u3, u3} TopologicalSpace.{u3} X)) (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (HasLiftT.mk.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (CoeTCₓ.coe.{succ u3, succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (Set.{u3} (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X)) (SetLike.Set.hasCoeT.{u3, u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) (coeSort.{succ (succ u3), succ (succ u3)} (CategoryTheory.Bundled.{u3, u3} TopologicalSpace.{u3}) Type.{u3} (CategoryTheory.Bundled.hasCoeToSort.{u3, u3} TopologicalSpace.{u3}) X) (TopologicalSpace.Opens.setLike.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))))) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))) (TopologicalSpace.Opens.map._proof_1.{u3} Y X (CategoryTheory.Iso.inv.{u3, succ u3} TopCat.{u3} TopCat.largeCategory.{u3} X Y H₁) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))))) (TopologicalSpace.Opens.mk_coe.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X) (Opposite.unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U))))) (Opposite.op_unop.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X)) U)) U U (rfl.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{succ u3, u3, u3} TopCat.{u3} TopCat.largeCategory.{u3} TopCat.concreteCategory.{u3}) X) (TopCat.topologicalSpace.{u3} X))) U)) (propext (Eq.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U U) True (eq_self_iff_true.{succ u3} (Opposite.{succ u3} (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} X) (TopCat.topologicalSpace.{u3} X))) U)))) trivial))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H₁ : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y) {ℱ : TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y} {𝒢 : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} (H₂ : Quiver.Hom.{max (succ u2) (succ u1), max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 Y))) ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) (U : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ)) U) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) U)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) ℱ) 𝒢 (TopCat.Presheaf.pushforwardToOfIso.{u2, u3, u1} C _inst_1 X Y H₁ ℱ 𝒢 H₂) U) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) U) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) C _inst_1 ℱ (TopCat.Presheaf.pushforwardObj.{u1, u2, u3} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) 𝒢) H₂ (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) (Prefunctor.map.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 𝒢) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) U (CategoryTheory.eqToHom.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y))))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.op.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.map.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Prefunctor.obj.{succ u1, succ u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)))))) (TopologicalSpace.Opens.map.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁))) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))) U (of_eq_true (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) U) (Eq.trans.{1} Prop (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) U) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) U) True (congrFun.{succ u1, 1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (fun (a._@.Init.Prelude._hyg.170 : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) => Prop) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (congrArg.{succ u1, succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) -> Prop) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (Eq.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))) (congrArg.{succ u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (Eq.ndrec.{0, succ u1} (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (fun (carrier : Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) => IsOpen.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) carrier) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) ((fun {α : Type.{u1}} [inst._@.Mathlib.Topology.Sets.Opens._hyg.47 : TopologicalSpace.{u1} α] (carrier : Set.{u1} α) (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => Eq.rec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier_1 : Set.{u1} α) (e_carrier : Eq.{succ u1} (Set.{u1} α) carrier carrier_1) => forall (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier), Eq.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open') (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier_1 (Eq.ndrec.{0, succ u1} (Set.{u1} α) carrier (fun (carrier : Set.{u1} α) => IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) is_open' carrier_1 e_carrier))) (fun (is_open' : IsOpen.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier) => Eq.refl.{succ u1} (TopologicalSpace.Opens.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47) (TopologicalSpace.Opens.mk.{u1} α inst._@.Mathlib.Topology.Sets.Opens._hyg.47 carrier is_open')) carrier_1 e_carrier) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U)) (congrFun.{succ u1, succ u1} (Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (fun (s : Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) => Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X)) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x))) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x)) (congrArg.{succ u1, succ u1} ((CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) -> (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) ((Set.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) -> (Set.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X))) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X)) (funext.{succ u1, succ u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) x)) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => x) (fun (x : CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) => CategoryTheory.FunctorToTypes.map_inv_map_hom_apply.{u1, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}) X Y H₁ x))) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (Opposite.op.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y)) (TopologicalSpace.Opens.mk.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} Y) (Set.preimage.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁)) (SetLike.coe.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopologicalSpace.Opens.instSetLikeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))) (TopologicalSpace.Opens.map.proof_1.{u1} Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H₁) (Opposite.unop.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) U))))))))) U) (eq_self.{succ u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) U))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_to_of_iso_app TopCat.Presheaf.pushforwardToOfIso_appₓ'. -/
 @[simp]
 theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf C} {𝒢 : X.Presheaf C}
     (H₂ : ℱ ⟶ H₁.Hom _* 𝒢) (U : (Opens X)ᵒᵖ) :
@@ -449,6 +647,12 @@ end Iso
 
 variable (C) [HasColimits C]
 
+/- warning: Top.presheaf.pullback -> TopCat.Presheaf.pullback is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback TopCat.Presheaf.pullbackₓ'. -/
 /-- Pullback a presheaf on `Y` along a continuous map `f : X ⟶ Y`, obtaining a presheaf
 on `X`. -/
 @[simps map_app]
@@ -456,18 +660,36 @@ def pullback {X Y : TopCat.{v}} (f : X ⟶ Y) : Y.Presheaf C ⥤ X.Presheaf C :=
   lan (Opens.map f).op
 #align Top.presheaf.pullback TopCat.Presheaf.pullback
 
+/- warning: Top.presheaf.pullback_obj_eq_pullback_obj -> TopCat.Presheaf.pullbackObj_eq_pullbackObj is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_3 : CategoryTheory.Category.{u1, u2} C] [_inst_4 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_3] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) (ℱ : TopCat.Presheaf.{u1, u1, u2} C _inst_3 Y), Eq.{succ (max u2 u1)} (TopCat.Presheaf.{u1, u1, u2} C _inst_3 X) (CategoryTheory.Functor.obj.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_3 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_3 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_3 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_3 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_3 _inst_4 X Y f) ℱ) (TopCat.Presheaf.pullbackObj.{u1, u2} C _inst_3 _inst_4 X Y f ℱ)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_3 : CategoryTheory.Category.{u2, u1} C] [_inst_4 : CategoryTheory.Limits.HasColimits.{u2, u1} C _inst_3] {X : TopCat.{u2}} {Y : TopCat.{u2}} (f : Quiver.Hom.{succ u2, succ u2} TopCat.{u2} (CategoryTheory.CategoryStruct.toQuiver.{u2, succ u2} TopCat.{u2} (CategoryTheory.Category.toCategoryStruct.{u2, succ u2} TopCat.{u2} instTopCatLargeCategory.{u2})) X Y) (ℱ : TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y), Eq.{max (succ u2) (succ u1)} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (Prefunctor.obj.{succ u2, succ u2, max u2 u1, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 Y))) (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 X))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u2 u1, max u2 u1} (TopCat.Presheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 Y) (TopCat.Presheaf.{u2, u2, u1} C _inst_3 X) (TopCat.instCategoryPresheaf.{u2, u2, u1} C _inst_3 X) (TopCat.Presheaf.pullback.{u2, u1} C _inst_3 _inst_4 X Y f)) ℱ) (TopCat.Presheaf.pullbackObj.{u2, u1} C _inst_3 _inst_4 X Y f ℱ)
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_obj_eq_pullback_obj TopCat.Presheaf.pullbackObj_eq_pullbackObjₓ'. -/
 @[simp]
 theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCat.{w}} (f : X ⟶ Y)
     (ℱ : Y.Presheaf C) : (pullback C f).obj ℱ = pullbackObj f ℱ :=
   rfl
 #align Top.presheaf.pullback_obj_eq_pullback_obj TopCat.Presheaf.pullbackObj_eq_pullbackObj
 
+/- warning: Top.presheaf.pushforward_pullback_adjunction -> TopCat.Presheaf.pushforwardPullbackAdjunction is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y), CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y f) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y f)
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y), CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y f) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunctionₓ'. -/
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
 def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
 
+/- warning: Top.presheaf.pullback_hom_iso_pushforward_inv -> TopCat.Presheaf.pullbackHomIsoPushforwardInv is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInvₓ'. -/
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/
 def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.Hom ≅ pushforward C H.inv :=
@@ -475,6 +697,12 @@ def pullbackHomIsoPushforwardInv {X Y : TopCat.{v}} (H : X ≅ Y) :
     (presheafEquivOfIso C H.symm).toAdjunction
 #align Top.presheaf.pullback_hom_iso_pushforward_inv TopCat.Presheaf.pullbackHomIsoPushforwardInv
 
+/- warning: Top.presheaf.pullback_inv_iso_pushforward_hom -> TopCat.Presheaf.pullbackInvIsoPushforwardHom is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.Presheaf.category.{u1, u1, u2} C _inst_1 Y)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Y H))
+but is expected to have type
+  forall (C : Type.{u2}) [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasColimits.{u1, u2} C _inst_1] {X : TopCat.{u1}} {Y : TopCat.{u1}} (H : CategoryTheory.Iso.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y), CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (TopCat.Presheaf.{u1, u1, u2} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 X) (TopCat.Presheaf.{u1, u1, u2} C _inst_1 Y) (TopCat.instCategoryPresheaf.{u1, u1, u2} C _inst_1 Y)) (TopCat.Presheaf.pullback.{u1, u2} C _inst_1 _inst_2 Y X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H)) (TopCat.Presheaf.pushforward.{u1, u1, u2} C _inst_1 X Y (CategoryTheory.Iso.hom.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y H))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.pullback_inv_iso_pushforward_hom TopCat.Presheaf.pullbackInvIsoPushforwardHomₓ'. -/
 /-- Pulling back along the inverse of a homeomorphism is the same as pushing forward along it. -/
 def pullbackInvIsoPushforwardHom {X Y : TopCat.{v}} (H : X ≅ Y) :
     pullback C H.inv ≅ pushforward C H.Hom :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

@@ -235,7 +235,7 @@ attribute [local tidy] tactic.op_induction'
 theorem id_hom_app (U) : (id ℱ).Hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) :=
   by
   -- was `tidy`
-  induction U using Opposite.rec
+  induction U using Opposite.rec'
   cases U
   rw [id_hom_app']
   congr

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

@@ -465,7 +465,7 @@ theorem pullbackObj_eq_pullbackObj {C} [Category C] [HasColimits C] {X Y : TopCa
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps unit_app_app counit_app_app]
 def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) : pullback C f ⊣ pushforward C f :=
-  lan.adjunction _ _
+  Lan.adjunction _ _
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction
 
 /-- Pulling back along a homeomorphism is the same as pushing forward along its inverse. -/

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

@@ -75,7 +75,7 @@ unsafe def restrict_attr : user_attribute (tactic Unit → tactic Unit) Unit
       dependencies := [] }
 #align Top.presheaf.restrict_attr Top.presheaf.restrict_attr
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 /-- A tactic to discharge goals of type `U ≤ V` for `Top.presheaf.restrict_open` -/
 unsafe def restrict_tac : ∀ n : ℕ, tactic Unit
   | 0 => tactic.fail "`restrict_tac` failed"
@@ -90,7 +90,7 @@ unsafe def restrict_tac' :=
 
 attribute [sheaf_restrict] bot_le le_top le_refl inf_le_left inf_le_right le_sup_left le_sup_right
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
 example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓ w) (h₂ : x ≤ y ⊓ z) : v ≤ y :=
   by
   run_tac
@@ -113,7 +113,7 @@ scoped[AlgebraicGeometry]
   notation:80 x " |_ₗ " U " ⟪" e "⟫ " =>
     @TopCat.Presheaf.restrict _ _ _ _ _ _ x U (@homOfLE (Opens _) _ U _ e)
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic Top.presheaf.restrict_tac' -/
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ U`, where the proof `U ≤ V` is inferred by
 the tactic `Top.presheaf.restrict_tac'` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -316,10 +316,9 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
     (H : IsOpen (f '' U)) : (pullbackObj f ℱ).obj (op U) ≅ ℱ.obj (op ⟨_, H⟩) :=
   by
   let x : costructured_arrow (opens.map f).op (op U) :=
-    { left := op ⟨f '' U, H⟩
-      Hom :=
-        ((@hom_of_le _ _ _ ((opens.map f).obj ⟨_, H⟩) (set.image_preimage.le_u_l _)).op :
-          op ((opens.map f).obj ⟨⇑f '' ↑U, H⟩) ⟶ op U) }
+    by
+    refine' @costructured_arrow.mk _ _ _ _ _ (op (opens.mk (f '' U) H)) _ _
+    exact (@hom_of_le _ _ _ ((opens.map f).obj ⟨_, H⟩) (set.image_preimage.le_u_l _)).op
   have hx : is_terminal x :=
     {
       lift := fun s => by

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.

@@ -346,8 +346,8 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
   have hx : IsTerminal x :=
     { lift := fun s ↦ by
         fapply CostructuredArrow.homMk
-        change op (unop _) ⟶ op (⟨_, H⟩ : Opens _)
-        · refine' (homOfLE _).op
+        · change op (unop _) ⟶ op (⟨_, H⟩ : Opens _)
+          refine' (homOfLE _).op
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
         · simp [autoParam, eq_iff_true_of_subsingleton]
@@ -419,8 +419,8 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
   · intros a b f
     ext U
     · erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
-      simp only [Functor.op_obj, eqToHom_refl, CategoryTheory.Functor.map_id,
-        Category.comp_id, Category.id_comp, Functor.id_obj, Functor.id_map]
+      · simp only [Functor.op_obj, eqToHom_refl, CategoryTheory.Functor.map_id,
+          Category.comp_id, Category.id_comp, Functor.id_obj, Functor.id_map]
       apply Pushforward.id_eq
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.id_pushforward TopCat.Presheaf.id_pushforward

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

@@ -7,7 +7,7 @@ import Mathlib.CategoryTheory.Limits.KanExtension
 import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
 

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.

@@ -42,7 +42,7 @@ variable (C : Type u) [Category.{v} C]
 namespace TopCat
 
 /-- The category of `C`-valued presheaves on a (bundled) topological space `X`. -/
--- Porting note: was @[nolint has_nonempty_instance]
+-- Porting note(#5171): was @[nolint has_nonempty_instance]
 def Presheaf (X : TopCat.{w}) : Type max u v w :=
   (Opens X)ᵒᵖ ⥤ C
 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".

@@ -42,7 +42,7 @@ variable (C : Type u) [Category.{v} C]
 namespace TopCat
 
 /-- The category of `C`-valued presheaves on a (bundled) topological space `X`. -/
--- porting note: was @[nolint has_nonempty_instance]
+-- Porting note: was @[nolint has_nonempty_instance]
 def Presheaf (X : TopCat.{w}) : Type max u v w :=
   (Opens X)ᵒᵖ ⥤ C
 set_option linter.uppercaseLean3 false in

Classifies by adding issue number #10756 to porting notes claiming added lemma.

@@ -58,7 +58,7 @@ namespace Presheaf
 @[simp] theorem comp_app {P Q R : Presheaf C X} (f : P ⟶ Q) (g : Q ⟶ R) :
     (f ≫ g).app U = f.app U ≫ g.app U := rfl
 
--- Porting note: added an `ext` lemma,
+-- Porting note (#10756): added an `ext` lemma,
 -- since `NatTrans.ext` can not see through the definition of `Presheaf`.
 -- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]

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

@@ -74,7 +74,7 @@ attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
 
 /-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>
-  `(attr|aesop safe 50 apply (rule_sets [$(Lean.mkIdent `Restrict):ident]))
+  `(attr|aesop safe 50 apply (rule_sets := [$(Lean.mkIdent `Restrict):ident]))
 
 attribute [sheaf_restrict] bot_le le_top le_refl inf_le_left inf_le_right
   le_sup_left le_sup_right
@@ -86,7 +86,7 @@ macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause* : tactic =>
     (config := { terminal := true
                  assumptionTransparency := .reducible
                  enableSimp := false })
-    (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
+    (rule_sets := [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
 /-- `restrict_tac?` passes along `Try this` from `aesop` -/
 macro (name := restrict_tac?) "restrict_tac?" c:Aesop.tactic_clause* : tactic =>
@@ -96,11 +96,11 @@ macro (name := restrict_tac?) "restrict_tac?" c:Aesop.tactic_clause* : tactic =>
                  assumptionTransparency := .reducible
                  enableSimp := false
                  maxRuleApplications := 300 })
-  (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
+  (rule_sets := [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
-attribute[aesop 10% (rule_sets [Restrict])] le_trans
-attribute[aesop safe destruct (rule_sets [Restrict])] Eq.trans_le
-attribute[aesop safe -50 (rule_sets [Restrict])] Aesop.BuiltinRules.assumption
+attribute[aesop 10% (rule_sets := [Restrict])] le_trans
+attribute[aesop safe destruct (rule_sets := [Restrict])] Eq.trans_le
+attribute[aesop safe -50 (rule_sets := [Restrict])] Aesop.BuiltinRules.assumption
 
 example {X} [CompleteLattice X] (v : Nat → X) (w x y z : X) (e : v 0 = v 1) (_ : v 1 = v 2)
     (h₀ : v 1 ≤ x) (_ : x ≤ z ⊓ w) (h₂ : x ≤ y ⊓ z) : v 0 ≤ y :=
@@ -258,8 +258,8 @@ set_option linter.uppercaseLean3 false in
 -- the proof below could be `by aesop_cat` if
 -- https://github.com/JLimperg/aesop/issues/59
 -- can be resolved, and we add:
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
+attribute [local aesop safe cases (rule_sets := [CategoryTheory])] Opposite
+attribute [local aesop safe cases (rule_sets := [CategoryTheory])] Opens
 
 @[simp]
 theorem id_hom_app (U) : (id ℱ).hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) := by

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.

@@ -138,7 +138,7 @@ set_option linter.uppercaseLean3 false in
 /-- restriction of a section to open subset -/
 scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
--- Porting note : linter tells this lemma is no going to be picked up by the simplifier, hence
+-- Porting note: linter tells this lemma is no going to be picked up by the simplifier, hence
 -- `@[simp]` is removed
 theorem restrict_restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
@@ -149,7 +149,7 @@ theorem restrict_restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategor
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.restrict_restrict TopCat.Presheaf.restrict_restrict
 
--- Porting note : linter tells this lemma is no going to be picked up by the simplifier, hence
+-- Porting note: linter tells this lemma is no going to be picked up by the simplifier, hence
 -- `@[simp]` is removed
 theorem map_restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
@@ -213,7 +213,7 @@ theorem pushforward_eq'_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y} (h : f = g) (
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward_eq'_hom_app TopCat.Presheaf.pushforward_eq'_hom_app
 
--- Porting note : This lemma is promoted to a higher priority to short circuit the simplifier
+-- Porting note: This lemma is promoted to a higher priority to short circuit the simplifier
 @[simp (high)]
 theorem pushforwardEq_rfl {X Y : TopCat.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq (rfl : f = f) ℱ).hom.app (op U) = 𝟙 _ := by
@@ -246,7 +246,7 @@ theorem id_eq : 𝟙 X _* ℱ = ℱ := by
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward.id_eq TopCat.Presheaf.Pushforward.id_eq
 
--- Porting note : This lemma is promoted to a higher priority to short circuit the simplifier
+-- Porting note: This lemma is promoted to a higher priority to short circuit the simplifier
 @[simp (high)]
 theorem id_hom_app' (U) (p) : (id ℱ).hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by
   dsimp [id]
@@ -351,7 +351,7 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
         · simp [autoParam, eq_iff_true_of_subsingleton]
-      -- porting note : add `fac`, `uniq` manually
+      -- Porting note: add `fac`, `uniq` manually
       fac := fun _ _ => by ext; simp [eq_iff_true_of_subsingleton]
       uniq := fun _ _ _ => by ext; simp [eq_iff_true_of_subsingleton] }
   exact IsColimit.coconePointUniqueUpToIso (colimit.isColimit _) (colimitOfDiagramTerminal hx _)
@@ -376,7 +376,7 @@ def id : pullbackObj (𝟙 _) ℱ ≅ ℱ :=
       erw [colimit.pre_desc_assoc, colimit.ι_desc_assoc, colimit.ι_desc_assoc]
       dsimp
       simp only [← ℱ.map_comp]
-      -- Porting note : `congr` does not work, but `congr 1` does
+      -- Porting note: `congr` does not work, but `congr 1` does
       congr 1
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pullback.id TopCat.Presheaf.Pullback.id
@@ -452,7 +452,7 @@ theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf
       ℱ.map (eqToHom (by simp [Opens.map, Set.preimage_preimage])) ≫
         H₂.app (op ((Opens.map H₁.inv).obj (unop U))) := by
   delta toPushforwardOfIso
-  -- Porting note : originally is a single invocation of `simp`
+  -- Porting note: originally is a single invocation of `simp`
   simp only [pushforwardObj_obj, Functor.op_obj, Equivalence.toAdjunction, Adjunction.homEquiv_unit,
     Functor.id_obj, Functor.comp_obj, Adjunction.mkOfUnitCounit_unit, unop_op, eqToHom_map]
   rw [NatTrans.comp_app, presheafEquivOfIso_inverse_map_app, Equivalence.Equivalence_mk'_unit]

• Remove Data.Set.Basic from scripts/noshake.json.
• Remove an exception that was used by examples only, move these examples to a new test file.
• Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
• Run lake exe shake --fix.

@@ -7,6 +7,7 @@ import Mathlib.CategoryTheory.Limits.KanExtension
 import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
+import Mathlib.Data.Set.Basic
 
 #align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
 

@@ -81,16 +81,20 @@ attribute [sheaf_restrict] bot_le le_top le_refl inf_le_left inf_le_right
 /-- `restrict_tac` solves relations among subsets (copied from `aesop cat`) -/
 macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause* : tactic =>
 `(tactic| first | assumption |
-  aesop $c* (options :=
-    { terminal := true, assumptionTransparency := .reducible })
-    (simp_options := { enabled := false })
-  (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
+  aesop $c*
+    (config := { terminal := true
+                 assumptionTransparency := .reducible
+                 enableSimp := false })
+    (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
 /-- `restrict_tac?` passes along `Try this` from `aesop` -/
 macro (name := restrict_tac?) "restrict_tac?" c:Aesop.tactic_clause* : tactic =>
 `(tactic|
-  aesop? $c* (options :=
-    { terminal := true, assumptionTransparency := .reducible, maxRuleApplications := 300 })
+  aesop? $c*
+    (config := { terminal := true
+                 assumptionTransparency := .reducible
+                 enableSimp := false
+                 maxRuleApplications := 300 })
   (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
 attribute[aesop 10% (rule_sets [Restrict])] le_trans

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>

@@ -5,7 +5,6 @@ Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 -/
 import Mathlib.CategoryTheory.Limits.KanExtension
 import Mathlib.Topology.Category.TopCat.Opens
-import Mathlib.Algebra.Category.Ring.Basic
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
 

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -70,7 +70,7 @@ lemma ext {P Q : Presheaf C X} {f g : P ⟶ Q} (w : ∀ U : Opens X, f.app (op U
   apply w
 
 attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
-  CategoryTheory.ConcreteCategory.instDFunLike
+  CategoryTheory.ConcreteCategory.instFunLike
 
 /-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -70,7 +70,7 @@ lemma ext {P Q : Presheaf C X} {f g : P ⟶ Q} (w : ∀ U : Opens X, f.app (op U
   apply w
 
 attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
-  CategoryTheory.ConcreteCategory.funLike
+  CategoryTheory.ConcreteCategory.instDFunLike
 
 /-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>

Various things break in the simpset for Presheaf when the simp algorithm changes in leanprover/lean4#3124. These backwards compatible fixes are, I think, improvements anyway.

One could further add a Presheaf.id_app lemma, and do further cleanup in the proofs which now use dsimp [-Presheaf.comp_app], but I'd prefer if these are done in a followup PR in order to not hold up #9500.

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

@@ -55,6 +55,9 @@ variable {C}
 
 namespace Presheaf
 
+@[simp] theorem comp_app {P Q R : Presheaf C X} (f : P ⟶ Q) (g : Q ⟶ R) :
+    (f ≫ g).app U = f.app U ≫ g.app U := rfl
+
 -- Porting note: added an `ext` lemma,
 -- since `NatTrans.ext` can not see through the definition of `Presheaf`.
 -- See https://github.com/leanprover-community/mathlib4/issues/5229
@@ -243,7 +246,7 @@ set_option linter.uppercaseLean3 false in
 @[simp (high)]
 theorem id_hom_app' (U) (p) : (id ℱ).hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (op ⟨U, p⟩)) := by
   dsimp [id]
-  simp [CategoryStruct.comp]
+  simp
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'
 
@@ -474,7 +477,7 @@ theorem pushforwardToOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : Y.Presheaf
     (pushforwardToOfIso H₁ H₂).app U =
       H₂.app (op ((Opens.map H₁.inv).obj (unop U))) ≫
         𝒢.map (eqToHom (by simp [Opens.map, Set.preimage_preimage])) := by
-  simp [pushforwardToOfIso, Equivalence.toAdjunction, CategoryStruct.comp]
+  simp [pushforwardToOfIso, Equivalence.toAdjunction]
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward_to_of_iso_app TopCat.Presheaf.pushforwardToOfIso_app
 

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

@@ -454,7 +454,7 @@ theorem toPushforwardOfIso_app {X Y : TopCat} (H₁ : X ≅ Y) {ℱ : X.Presheaf
     Functor.id_obj, Functor.comp_obj, Iso.symm_hom, NatIso.op_inv, Iso.symm_inv, NatTrans.op_app,
     NatIso.ofComponents_hom_app, eqToIso.hom, eqToHom_op, Equivalence.Equivalence_mk'_unitInv,
     Equivalence.Equivalence_mk'_counitInv, NatIso.op_hom, unop_op, op_unop, eqToIso.inv,
-    NatIso.ofComponents_inv_app, eqToHom_unop, ←ℱ.map_comp, eqToHom_trans, eqToHom_map,
+    NatIso.ofComponents_inv_app, eqToHom_unop, ← ℱ.map_comp, eqToHom_trans, eqToHom_map,
     presheafEquivOfIso_unitIso_hom_app_app]
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.to_pushforward_of_iso_app TopCat.Presheaf.toPushforwardOfIso_app

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -343,7 +343,7 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
         · refine' (homOfLE _).op
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
-        · simp [eq_iff_true_of_subsingleton]
+        · simp [autoParam, eq_iff_true_of_subsingleton]
       -- porting note : add `fac`, `uniq` manually
       fac := fun _ _ => by ext; simp [eq_iff_true_of_subsingleton]
       uniq := fun _ _ _ => by ext; simp [eq_iff_true_of_subsingleton] }

Fixed AlgebraicGeometry/AffineSchemes.lean, AlgebraicGeometry/Morphisms/QuasiSeparated.lean and AlgebraicGeometry/Morphisms/RingHomProperties.lean.

Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -5,6 +5,7 @@ Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 -/
 import Mathlib.CategoryTheory.Limits.KanExtension
 import Mathlib.Topology.Category.TopCat.Opens
+import Mathlib.Algebra.Category.Ring.Basic
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
 
@@ -70,26 +71,33 @@ attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
 
 /-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>
-  `(attr|aesop safe apply (rule_sets [$(Lean.mkIdent `Restrict):ident]))
+  `(attr|aesop safe 50 apply (rule_sets [$(Lean.mkIdent `Restrict):ident]))
 
 attribute [sheaf_restrict] bot_le le_top le_refl inf_le_left inf_le_right
   le_sup_left le_sup_right
 
 /-- `restrict_tac` solves relations among subsets (copied from `aesop cat`) -/
 macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause* : tactic =>
-`(tactic|
-  aesop $c* (options := { introsTransparency? := some .default, terminal := true })
-  (rule_sets [$(Lean.mkIdent `Restrict):ident]))
+`(tactic| first | assumption |
+  aesop $c* (options :=
+    { terminal := true, assumptionTransparency := .reducible })
+    (simp_options := { enabled := false })
+  (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
 /-- `restrict_tac?` passes along `Try this` from `aesop` -/
 macro (name := restrict_tac?) "restrict_tac?" c:Aesop.tactic_clause* : tactic =>
 `(tactic|
-  aesop? $c* (options := { introsTransparency? := some .default, terminal := true })
-  (rule_sets [$(Lean.mkIdent `Restrict):ident]))
+  aesop? $c* (options :=
+    { terminal := true, assumptionTransparency := .reducible, maxRuleApplications := 300 })
+  (rule_sets [-default, -builtin, $(Lean.mkIdent `Restrict):ident]))
 
-example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓ w) (h₂ : x ≤ y ⊓ z) : v ≤ y :=
-  by restrict_tac
+attribute[aesop 10% (rule_sets [Restrict])] le_trans
+attribute[aesop safe destruct (rule_sets [Restrict])] Eq.trans_le
+attribute[aesop safe -50 (rule_sets [Restrict])] Aesop.BuiltinRules.assumption
 
+example {X} [CompleteLattice X] (v : Nat → X) (w x y z : X) (e : v 0 = v 1) (_ : v 1 = v 2)
+    (h₀ : v 1 ≤ x) (_ : x ≤ z ⊓ w) (h₂ : x ≤ y ⊓ z) : v 0 ≤ y :=
+  by restrict_tac
 
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

@@ -335,10 +335,10 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
         · refine' (homOfLE _).op
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
-        · simp
+        · simp [eq_iff_true_of_subsingleton]
       -- porting note : add `fac`, `uniq` manually
-      fac := fun _ _ => by ext; simp
-      uniq := fun _ _ _ => by ext; simp }
+      fac := fun _ _ => by ext; simp [eq_iff_true_of_subsingleton]
+      uniq := fun _ _ _ => by ext; simp [eq_iff_true_of_subsingleton] }
   exact IsColimit.coconePointUniqueUpToIso (colimit.isColimit _) (colimitOfDiagramTerminal hx _)
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pullback_obj_obj_of_image_open TopCat.Presheaf.pullbackObjObjOfImageOpen

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

@@ -185,7 +185,7 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem pushforwardEq_hom_app {X Y : TopCat.{w}} {f g : X ⟶ Y}
-  (h : f = g) (ℱ : X.Presheaf C) (U) :
+    (h : f = g) (ℱ : X.Presheaf C) (U) :
     (pushforwardEq h ℱ).hom.app U =
       ℱ.map (by dsimp [Functor.op]; apply Quiver.Hom.op; apply eqToHom; rw [h]) :=
   by simp [pushforwardEq]

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

@@ -494,7 +494,7 @@ set_option linter.uppercaseLean3 false in
 /-- The pullback and pushforward along a continuous map are adjoint to each other. -/
 @[simps! unit_app_app counit_app_app]
 def pushforwardPullbackAdjunction {X Y : TopCat.{v}} (f : X ⟶ Y) :
-  pullback C f ⊣ pushforward C f :=
+    pullback C f ⊣ pushforward C f :=
   Lan.adjunction _ _
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward_pullback_adjunction TopCat.Presheaf.pushforwardPullbackAdjunction

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

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

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

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

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

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

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

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

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

@@ -29,6 +29,8 @@ We also define the functors `pushforward` and `pullback` between the categories
 `TopCat.Presheaf.pushforwardPullbackAdjunction`.
 -/
 
+set_option autoImplicit true
+
 
 universe w v u
 

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

This has nice performance benefits.

@@ -93,7 +93,7 @@ example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓
 For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
 and the notation `x |_ₗ U ⟪i⟫` (`l` stands for `le`) for `i : U ≤ V`.
 -/
-def restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C] {F : X.Presheaf C}
+def restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C] {F : X.Presheaf C}
     {V : Opens X} (x : F.obj (op V)) {U : Opens X} (h : U ⟶ V) : F.obj (op U) :=
   F.map h.op x
 set_option linter.uppercaseLean3 false in
@@ -110,7 +110,7 @@ open AlgebraicGeometry
 /-- The restriction of a section along an inclusion of open sets.
 For `x : F.obj (op V)`, we provide the notation `x |_ U`, where the proof `U ≤ V` is inferred by
 the tactic `Top.presheaf.restrict_tac'` -/
-abbrev restrictOpen {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C] {F : X.Presheaf C}
+abbrev restrictOpen {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C] {F : X.Presheaf C}
     {V : Opens X} (x : F.obj (op V)) (U : Opens X)
     (e : U ≤ V := by restrict_tac) :
     F.obj (op U) :=
@@ -123,7 +123,7 @@ scoped[AlgebraicGeometry] infixl:80 " |_ " => TopCat.Presheaf.restrictOpen
 
 -- Porting note : linter tells this lemma is no going to be picked up by the simplifier, hence
 -- `@[simp]` is removed
-theorem restrict_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
+theorem restrict_restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C]
     {F : X.Presheaf C} {U V W : Opens X} (e₁ : U ≤ V) (e₂ : V ≤ W) (x : F.obj (op W)) :
     x |_ V |_ U = x |_ U := by
   delta restrictOpen restrict
@@ -134,7 +134,7 @@ set_option linter.uppercaseLean3 false in
 
 -- Porting note : linter tells this lemma is no going to be picked up by the simplifier, hence
 -- `@[simp]` is removed
-theorem map_restrict {X : TopCat} {C : Type _} [Category C] [ConcreteCategory C]
+theorem map_restrict {X : TopCat} {C : Type*} [Category C] [ConcreteCategory C]
     {F G : X.Presheaf C} (e : F ⟶ G) {U V : Opens X} (h : U ≤ V) (x : F.obj (op V)) :
     e.app _ (x |_ U) = e.app _ x |_ U := by
   delta restrictOpen restrict

Adds aesop_cat? aesop_graph? and restrict_tac?

@@ -79,6 +79,12 @@ macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause* : tactic =>
   aesop $c* (options := { introsTransparency? := some .default, terminal := true })
   (rule_sets [$(Lean.mkIdent `Restrict):ident]))
 
+/-- `restrict_tac?` passes along `Try this` from `aesop` -/
+macro (name := restrict_tac?) "restrict_tac?" c:Aesop.tactic_clause* : tactic =>
+`(tactic|
+  aesop? $c* (options := { introsTransparency? := some .default, terminal := true })
+  (rule_sets [$(Lean.mkIdent `Restrict):ident]))
+
 example {X : TopCat} {v w x y z : Opens X} (h₀ : v ≤ x) (h₁ : x ≤ z ⊓ w) (h₂ : x ≤ y ⊓ z) : v ≤ y :=
   by restrict_tac
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
-
-! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.KanExtension
 import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
 
+#align_import topology.sheaves.presheaf from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
+
 /-!
 # Presheaves on a topological space
 

This PR is the result of running

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

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

@@ -327,10 +327,10 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
     { lift := fun s ↦ by
         fapply CostructuredArrow.homMk
         change op (unop _) ⟶ op (⟨_, H⟩ : Opens _)
-        . refine' (homOfLE _).op
+        · refine' (homOfLE _).op
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
-        . simp
+        · simp
       -- porting note : add `fac`, `uniq` manually
       fac := fun _ _ => by ext; simp
       uniq := fun _ _ _ => by ext; simp }
@@ -398,7 +398,7 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
   apply CategoryTheory.Functor.ext
   · intros a b f
     ext U
-    . erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
+    · erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
       simp only [Functor.op_obj, eqToHom_refl, CategoryTheory.Functor.map_id,
         Category.comp_id, Category.id_comp, Functor.id_obj, Functor.id_map]
       apply Pushforward.id_eq

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.sheaves.presheaf
-! leanprover-community/mathlib commit 8a318021995877a44630c898d0b2bc376fceef3b
+! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

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

@@ -55,6 +55,17 @@ variable {C}
 
 namespace Presheaf
 
+-- Porting note: added an `ext` lemma,
+-- since `NatTrans.ext` can not see through the definition of `Presheaf`.
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
+@[ext]
+lemma ext {P Q : Presheaf C X} {f g : P ⟶ Q} (w : ∀ U : Opens X, f.app (op U) = g.app (op U)) :
+    f = g := by
+  apply NatTrans.ext
+  ext U
+  induction U with | _ U => ?_
+  apply w
+
 attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
   CategoryTheory.ConcreteCategory.funLike
 
@@ -386,9 +397,8 @@ set_option linter.uppercaseLean3 false in
 theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presheaf C) := by
   apply CategoryTheory.Functor.ext
   · intros a b f
-    -- porting note : `ext` does not see this
-    refine NatTrans.ext _ _ (funext fun U => ?_)
-    . erw [NatTrans.congr f (Opens.op_map_id_obj U)]
+    ext U
+    . erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
       simp only [Functor.op_obj, eqToHom_refl, CategoryTheory.Functor.map_id,
         Category.comp_id, Category.id_comp, Functor.id_obj, Functor.id_map]
       apply Pushforward.id_eq

Closes #4551.

Essentially op_induction is not necessary, now that Opposite.rec' is labelled with @[eliminator]. It would be nice if we could use this from inside aesop, see https://github.com/JLimperg/aesop/issues/59.

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

@@ -223,12 +223,17 @@ theorem id_hom_app' (U) (p) : (id ℱ).hom.app (op ⟨U, p⟩) = ℱ.map (𝟙 (
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward.id_hom_app' TopCat.Presheaf.Pushforward.id_hom_app'
 
--- porting note: TODO: attribute [local tidy] tactic.op_induction'
+-- Porting note:
+-- the proof below could be `by aesop_cat` if
+-- https://github.com/JLimperg/aesop/issues/59
+-- can be resolved, and we add:
+attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
+attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
 
 @[simp]
 theorem id_hom_app (U) : (id ℱ).hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) := by
-  -- was `tidy`
-  induction' U with U
+  -- was `tidy`, see porting note above.
+  induction U
   apply id_hom_app'
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app

@@ -56,7 +56,7 @@ variable {C}
 namespace Presheaf
 
 attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
-  CategoryTheory.ConcreteCategory.hasCoeToFun
+  CategoryTheory.ConcreteCategory.funLike
 
 /-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>

These are all doc fixes

@@ -58,7 +58,7 @@ namespace Presheaf
 attribute [local instance] CategoryTheory.ConcreteCategory.hasCoeToSort
   CategoryTheory.ConcreteCategory.hasCoeToFun
 
-/-- attribute `sheaf_restrict` to mark lemmas related to restricting sheafs -/
+/-- attribute `sheaf_restrict` to mark lemmas related to restricting sheaves -/
 macro "sheaf_restrict" : attr =>
   `(attr|aesop safe apply (rule_sets [$(Lean.mkIdent `Restrict):ident]))
 

@@ -16,20 +16,20 @@ import Mathlib.Topology.Sheaves.Init
 /-!
 # Presheaves on a topological space
 
-We define `presheaf C X` simply as `(opens X)ᵒᵖ ⥤ C`,
+We define `TopCat.Presheaf C X` simply as `(TopologicalSpace.Opens X)ᵒᵖ ⥤ C`,
 and inherit the category structure with natural transformations as morphisms.
 
 We define
-* `pushforward_obj {X Y : Top.{w}} (f : X ⟶ Y) (ℱ : X.presheaf C) : Y.presheaf C`
+* `TopCat.Presheaf.pushforwardObj {X Y : Top.{w}} (f : X ⟶ Y) (ℱ : X.Presheaf C) : Y.Presheaf C`
 with notation `f _* ℱ`
-and for `ℱ : X.presheaf C` provide the natural isomorphisms
-* `pushforward.id : (𝟙 X) _* ℱ ≅ ℱ`
-* `pushforward.comp : (f ≫ g) _* ℱ ≅ g _* (f _* ℱ)`
+and for `ℱ : X.Presheaf C` provide the natural isomorphisms
+* `TopCat.Presheaf.Pushforward.id : (𝟙 X) _* ℱ ≅ ℱ`
+* `TopCat.Presheaf.Pushforward.comp : (f ≫ g) _* ℱ ≅ g _* (f _* ℱ)`
 along with their `@[simp]` lemmas.
 
 We also define the functors `pushforward` and `pullback` between the categories
-`X.presheaf C` and `Y.presheaf C`, and provide their adjunction at
-`pushforward_pullback_adjunction`.
+`X.Presheaf C` and `Y.Presheaf C`, and provide their adjunction at
+`TopCat.Presheaf.pushforwardPullbackAdjunction`.
 -/
 
 

Mostly this is installing the Opposite.rec' induction principle as the default @[eliminator], but also many other fixes and removing unnecessary steps from proofs.

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

@@ -228,7 +228,7 @@ set_option linter.uppercaseLean3 false in
 @[simp]
 theorem id_hom_app (U) : (id ℱ).hom.app U = ℱ.map (eqToHom (Opens.op_map_id_obj U)) := by
   -- was `tidy`
-  induction' U using Opposite.rec' with U
+  induction' U with U
   apply id_hom_app'
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.pushforward.id_hom_app TopCat.Presheaf.Pushforward.id_hom_app

This fixes a bunch of spacing bugs in tactics. Mathlib counterpart of:

• Lean: leanprover/lean4#2240
• Std: leanprover/std4#149
• Aesop: JLimperg/aesop#56

@@ -66,7 +66,7 @@ attribute [sheaf_restrict] bot_le le_top le_refl inf_le_left inf_le_right
   le_sup_left le_sup_right
 
 /-- `restrict_tac` solves relations among subsets (copied from `aesop cat`) -/
-macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause*: tactic =>
+macro (name := restrict_tac) "restrict_tac" c:Aesop.tactic_clause* : tactic =>
 `(tactic|
   aesop $c* (options := { introsTransparency? := some .default, terminal := true })
   (rule_sets [$(Lean.mkIdent `Restrict):ident]))

@@ -9,7 +9,7 @@ Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
 ! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.KanExtension
-import Mathlib.Topology.Category.Top.Opens
+import Mathlib.Topology.Category.TopCat.Opens
 import Mathlib.CategoryTheory.Adjunction.Opposites
 import Mathlib.Topology.Sheaves.Init
 

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>